Connecticut's legislature is drafting a law that would enable this adoption. But regardless of what state you live in, some judges will award second-parent adoptions and others will not. Other judges refuse to grant such adoptions or make the process extremely difficult. Further, each state's family laws and adoption proceedings are unique. See a lawyer who is familiar with your state's lesbian and gay family law.
Nothing is as safe as a legal adoption.
As thoroughly as you can, document your joint involvement in creating and caring for your child. Both of you should sign and date this agreement. Type up a series of consent forms in which the legal parent authorizes the co-parent to oversee the child's health, medical, school and other procedures and events. Have the legal parent sign these documents. The legal parent must write a will or codicil nominating the co-parent to be the child's guardian if the legal parent dies.