According to
this article in the law journal of Villanova University, it is not in the public domain (at least, Balanchine's version). The ballet is wholly owned by Leda Eglevsky - though I think she has died so it has probably devolved to her heirs, and may still be administered by the Trust.
It might make sense to ask someone at ABT - since it is in their repertory, they would would know who they contact for permission to perform it.