<PAGE>   1

                                                               EXHIBIT 3.1


              TWELFTH AMENDMENT TO AGREEMENT OF LIMITED PARTNERSHIP
                     OF SUMMIT PROPERTIES PARTNERSHIP, L.P.


         This TWELFTH AMENDMENT TO AGREEMENT OF LIMITED PARTNERSHIP OF SUMMIT
PROPERTIES PARTNERSHIP, L.P. (this "Amendment") dated as of May 22, 1998, is
entered into by and among Summit Properties Inc. (the "Company") and the Persons
whose names are set forth on Exhibit A or Exhibit B as attached hereto. All
capitalized terms contained herein and not otherwise defined herein shall have
the meaning attributed to them in the Agreement.

         WHEREAS, the Company and the Persons whose names are set forth on
Exhibit A, other than certain of the New Partners (the "Existing Partners") are
partners of Summit Properties Partnership, L.P. (the "Partnership") pursuant to
an Agreement of Limited Partnership dated as of January 29, 1994, as previously
amended (as amended, the "Agreement"); and

         WHEREAS, Summit is to receive a contribution of an undivided interest
in Legacy Square Apartments now held by TCR Legacy Square Limited Partnership
("Crow") in exchange for each of the Persons whose names are set forth on
Exhibit B (the "New Partners"), all of whom are partners in Crow, being admitted
to the Partnership as an Additional Limited Partner pursuant to Section 12.2 of
the Agreement (unless such person already is a partner of the Partnership) and
receiving the Partnership Units set forth opposite their names on Exhibit B
attached hereto; and

         WHEREAS, the Company, the Existing Partners and the New Partners desire
to cause the Agreement to be amended to reflect the admission of the New
Partners and the issuance of the Partnership Units to the New Partners.

         NOW, THEREFORE, in accordance with the provisions of Section 4.2,
Section 12.2 and Section 12.3 of the Agreement, the Agreement is hereby amended
(a) to admit as an Additional Limited Partner each of the New Partners who is
not currently a partner of the Partnership and (b) to substitute the Exhibit A
attached hereto for the Exhibit A attached to the Agreement. Except as expressly
amended by the provisions hereof or as may be necessary to effect the intent of
the parties as evidenced by this Amendment, all other terms and provisions of
the Agreement are hereby ratified and confirmed and remain in full force and
effect.


<PAGE>   2



         IN WITNESS WHEROF, the parties hereto have executed this Amendment as
of the date first above written.

                         GENERAL PARTNER:

                         SUMMIT PROPERTIES INC.


                         By:    /s/ Doug Brout
                                ---------------------
                         Name:  Doug Brout
                                ---------------------
                         Title: Vice President
                                ---------------------


                         EXISTING PARTNERS:

                         Those persons listed on Exhibit A
                         attached hereto other than persons
                         signing below as New Partners

                         By: Summit Properties Inc., 
                             their attorney-in-fact

                             By:    /s/ Doug Brout
                                    ---------------------
                             Name:  Doug Brout
                                    ---------------------
                             Title: Vice President
                                    ---------------------



<PAGE>   3

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.

                                TCR LEGACY SQUARE LIMITED PARTNERSHIP

                                By: TCR Atlanta 1996, Inc., 
                                    its general partner

                                    By:    /s/ Thomas J. Patterson
                                           -------------------------------
                                    Name:  Thomas J. Patterson
                                           -------------------------------
                                    Title: Vice President 
                                           -------------------------------

<PAGE>   4

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.


                                    /s/ J. Ronald Terwilliger
                                    -------------------------------
                                    J. Ronald Terwilliger




<PAGE>   5

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.


                                    /s/ Randy J. Pace
                                    -------------------------------
                                    Randy J. Pace



<PAGE>   6


                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.


                                    /s/ David J. Elwell
                                    -------------------------------
                                    David J. Elwell



<PAGE>   7

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.


                                    /s/ Leonard W. Wood
                                    -------------------------------
                                    Leonard W. Wood



<PAGE>   8

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.


                                    /s/ Harlan R. Crow
                                    -------------------------------
                                    Harlan R. Crow



<PAGE>   9

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.


                                LEONARD W. WOOD FAMILY LIMITED PARTNERSHIP

                                By: /s/ Leonard W. Wood
                                    -------------------------------
                                    Leonard W. Wood, General Partner



<PAGE>   10

                       SUMMIT PROPERTIES PARTNERSHIP, L.P.

                                 SIGNATURE PAGE

                TO BE EXECUTED BY EACH ADDITIONAL LIMITED PARTNER


         The undersigned hereby executes this Signature Page to the Agreement of
Limited Partnerships dated as of January 29, 1994, as subsequently amended (the
"Agreement") of Summit Properties Partnership, L.P., a Delaware limited
partnership, for the purpose of being admitted to said Limited Partnership, as a
Limited Partner, and the undersigned does further hereby adopt, accept, ratify,
confirm and agree to be bound by all of the terms and conditions of said
Agreement applicable to it as a Limited Partner, including, without limitation,
the provisions of Section 2.4 and any other provision of the Agreement
appointing the General Partner or the Liquidator (as those terms are defined in
the Agreement) as attorney-in-fact for the undersigned.



                           CFP RESIDENTIAL

                           By: Crow Family, Inc., its general partner


                                By:    /s/ Sarah Puckett
                                       -------------------------------
                                Name:  Sarah Puckett
                                       -------------------------------
                                Title: Vice President
                                       -------------------------------