That is a very interesting question and not one that I regularly see. Understand that the prohibition against firearm possession for a domestic violence charge relates to federal law and not CO state law. I was a judge in Cortez for several years and, to my knowledge, people who had DV convictions in front of me still obtained bow hunting licenses to hunt without a problem. However, I will also defer to some of my colleagues who are either hunters or who represent hunters on a more frequent basis.
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Thus far, the only statutorily specific weapon possession prohibition affecting anyone convicted of "a misdemeanor crime of domestic violence" is a firearm. (Lautenberg Amendment, 1996) (arguably a bill of attainder and ex post facto law as applied to any convictions before the date of enactment - but that's another story). Generally, again, thus far, the issuance of a hunting license is not dependent upon a person's eligibility (or not) to possess a firearm or any other hunting tool. So, at this time, the answer is probably "yes."
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