Following a state or federal conviction for a felony offense, the loses certain constitutional rights, including the right to vote, the right to run for public office and the right to bear arms. By applying for a restoration of rights, a convicted felon may have his rights to vote and run for public office restored, however, the right to bear arms is seldom restored.
Some states will not restrict a convicted felon from applying for or purchasing a hunting license. While some states, including Wisconsin and Arkansas, have investigated the possibility of running background checks on hunting license applicants and restricting their purchase, most states will allow a convicted felon to purchase a hunting license.
The primary obstacles to hunting for convicted felons are laws restricting felons' ability to exercise their Second Amendment right to bear arms. In other words, in almost all circumstances, felons are prohibited from possessing firearms and most hunters use guns to hunt. Federal law prohibits any convicted felon to possess a gun. Federal law is only applicable is the purchase or acquisition of the firearm involved interstate commerce. Even if federal law is inapplicable, most states outlaw felons from possessing firearms.
While a convicted felon may have trouble purchasing a gun, some third parties have tried to assist felons by purchasing a firearm in their own name and then making the firearm available to the felon. This is called a straw-man purchase and is illegal for the felon and for the third party.
Under federal law, bows and cross-bows are not considered firearms. This means that under federal law, a convicted felon, if able to procure a hunting license in their state, would be legally permitted to hunt with a cross-bow. However, some states, including New York, separately prohibit convicted felons from possession for weapons, such as cross-bows. It is important to find out your state's laws on felon possession of these weapons.
The best way to find out whether or not a convicted felon can hunt with a firearm, a bow, or a cross-bow in your local jurisdiction is to consult with the local authorities, or with a local attorney knowledgeable on these topics. Ignorance or misunderstanding of the law is not a valid legal defense for breaking the law.