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 the abuser may have been convicted, you can go to the courthouse and ask the clerk of court for access to those records.
Federal law specifically prohibits possession of a firearm if the person is convicted of any felony or of a domestic violence misdemeanor. Criminal records that would make a person ineligible to purchase a firearm 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 purchase a gun?