Second degree animal cruelty is a gross misdemeanor offense, so that may indeed be what you were convicted of committing. The maximum penalty for that is 364 days in county jail. As a result, your conviction would not trigger the federal firearm ban under 18 U.S.C. § 922(g) since the conviction would need to be a felony offense (which includes a state designated misdemeanor if the offense is punishable by 2 or more years imprisonment) or a conviction on a crime of domestic violence and this offense is neither of those. Similarly Washington only prohibits possession of a firearm by persons convicted of specified felonies listed in the statute. So if it was a gross misdemeanor you should fine.

