Well, according to the New York State Department of Environmental Conservation, the law authorizing crossbow hunting for big game expires at the end of the year. See http://www.dec.ny.gov/outdoor/68802.html
Additionally, if you are on parole, you did not mention that but, if you are, you have to abide by the conditions of the parole which may prohibit the possession and/or ownership of any weapons.
With respect to moving to another state, which law applies, that is an open question because you did not mention the state. But, generally, using "Comity" which is part of the Privileges and Immunities Clause in Article Four of the United States Constitution, the other state will give the laws of New York effect. In other words, they will abide by the New York judgment of you EXCEPT if the New York law is in conflict with their own state law.
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