The Supreme Court decision in Everson v. Board of Education stated that the First Amendment means at least this. These words were repeated again in three later Supreme Court decisions.
"Neither the state nor the Federal Government can set up a church. Neither can pass laws which aid one religion, aid all religions, or prefer one religion over another. Neither can force nor influence a person to go to or remain away from church against his will or force him to profess a belief or disbelief in any religion. No person can be punished for entertaining or professing religious beliefs or disbeliefs, for church attendance or nonattendance. No tax in any amount, large or small, can be levied to support any religious activities or institutions, whatever they may be called, or whatever form they may adopt to teach or practice religion. Neither a state nor the Federal Government can, openly or secretly, participate in the affairs of any religious organizations or groups and vice versa. In the words of Jefferson, the clause against establishment of religion by law was intended to erect 'a wall of separation between church and state.'"
On the state level we have a New York State Constitution. Article XI, Section 3, states: "Neither the state nor any subdivision thereof shall use its property or credit or any public money, or authorize or permit either to be used, directly or indirectly, in aid or maintenance, other than for examination and inspection, of any school or institution of learning, in whole or in part under the control or direction of any religious denomination or in which any denominational tenet or doctrine is taught, but the legislature may provide for the transportation of children to and from any school or institution of learning." This bit about bussing was added in 1938.
(Most other states have some similar wording.)
Americans United for Separation of Church and State
3553 West Ridge Road,