A paper sheet handling apparatus comprising: a service mechanism unit for delivery of a paper sheet or sheets; a counting processing unit for counting of the paper sheet or sheets; a stacker for storing of the paper sheet or sheets; a conveyance path (10a-10e, 40a, 40b) for conveyance of the paper sheet or sheets to the service mechanism unit, the counting processing unit and the stacker; a delivery connection provided between the conveyance path (10a-10e, 40a, 40b) and the stacker to perform delivery of a paper sheet or sheets; and connection switching means (59, 60, 62, S), configured to perform a switching operation, wherein the delivery connection is switched between a connected state, in which the delivery connection is connected to the conveyance path (10a-10e, 40a, 40b) and the stacker to enable delivery of a paper sheet or sheets, and an evacuated state to release the connection, characterized in that: a direction, in which the connection switching means (59, 60, 62, S) is configured to perform the switching operation of the delivery connection, is structured in a direction along a delivery direction of a paper sheet or sheets between the conveyance path (10a-10e, 40a, 40b) and the stacker; wherein the delivery connection is pivotally supported by a rotating shaft which is provided on a side of the conveyance path (10a-10e, 40a, 40b) so as to turn the switching operation, and the rotating shaft is configured always to abut against a positioning part of the counting processing unit, which is provided on the side of the conveyance path (10a-10e, 40a, 40b) and by which the connection switching means (59, 60, 62, S) is positioned relative to the stacker, at least in the connected state. a service mechanism unit for delivery of a paper sheet or sheets; a counting processing unit for counting of the paper sheet or sheets; a stacker for storing of the paper sheet or sheets; a conveyance path (10a-10e, 40a, 40b) for conveyance of the paper sheet or sheets to the service mechanism unit, the counting processing unit and the stacker; a delivery connection provided between the conveyance path (10a-10e, 40a, 40b) and the stacker to perform delivery of a paper sheet or sheets; and connection switching means (59, 60, 62, S), configured to perform a switching operation, wherein the delivery connection is switched between a connected state, in which the delivery connection is connected to the conveyance path (10a-10e, 40a, 40b) and the stacker to enable delivery of a paper sheet or sheets, and an evacuated state to release the connection, characterized in that: a direction, in which the connection switching means (59, 60, 62, S) is configured to perform the switching operation of the delivery connection, is structured in a direction along a delivery direction of a paper sheet or sheets between the conveyance path (10a-10e, 40a, 40b) and the stacker; wherein the delivery connection is pivotally supported by a rotating shaft which is provided on a side of the conveyance path (10a-10e, 40a, 40b) so as to turn the switching operation, and the rotating shaft is configured always to abut against a positioning part of the counting processing unit, which is provided on the side of the conveyance path (10a-10e, 40a, 40b) and by which the connection switching means (59, 60, 62, S) is positioned relative to the stacker, at least in the connected state. a direction, in which the connection switching means (59, 60, 62, S) is configured to perform the switching operation of the delivery connection, is structured in a direction along a delivery direction of a paper sheet or sheets between the conveyance path (10a-10e, 40a, 40b) and the stacker; wherein the delivery connection is pivotally supported by a rotating shaft which is provided on a side of the conveyance path (10a-10e, 40a, 40b) so as to turn the switching operation, and the rotating shaft is configured always to abut against a positioning part of the counting processing unit, which is provided on the side of the conveyance path (10a-10e, 40a, 40b) and by which the connection switching means (59, 60, 62, S) is positioned relative to the stacker, at least in the connected state.