Sure she does...unless she is a member of the Congress, and it involves setting up a state religion.
If not, we would not have a continuing series of questions in the courts to address the ramifications, such as the "public access" ruling that allowed student Christian bible study groups to use school facilities.
And the First Amendment extends to the STATES as well as the Federal government. That, too, has long been established.
Perhaps you could bone up a bit on Constitutional law. I know that many far, far right fanatics like to scream about "strict interpretation," but the majority of us conservatives are glad that there has been some elucidation over the decades.
Are you suggesting that the town where you live, could establish a "town church" funded with city taxes? After all, your town isn't Congress, right?