If the abuser has been convicted of a crime, can s/he legally keep or buy a gun?
NY state law says that a person can NEVER have a "rifle or shotgun" if s/he has been convicted of a felony or serious offense.1 Also, a person cannot have any "firearm" outside of his/her home or place of business if s/he has been convicted of a felony or a class A misdemeanor within the past five years.2
1 NY Penal Law § 265.01(4)
2 NY Penal Law § 265.02(5)(ii)
How can I find out if the abuser has been convicted of a crime?
Misdemeanor and felony records are open to the public, but they are not always easy to access. If you know the exact courthouse where your abuser may have been convicted, you can go to the courthouse and ask the clerk of court for access to those records.
Domestic violence misdemeanor and felony records are also kept in the National Instant Criminal Background Check System (NICS). However, no one other than law enforcement officials and licensed firearm sellers are allowed to search the NICS. Your local police department may be willing to search NICS for you if you ask, but they are not required to do so.
To read more about the NICS, please see the question What will happen if the abuser tries to buy a gun when s/he isn't supposed to?