The National Park Service has a two-prong mission. To preserve the natural resources and provide for people to enjoy them. When it comes to fishing, the agency simultaneously wants to protect rare and native fisheries, while allowing people to catch, and sometimes kill and eat, fish. Check with the regulations of individual parks for specific regulations. Sometimes, one doesn’t even need a state fishing license to fish in national parks, but parks often have stricter regulations about, for example, regarding bait or non-toxic tackle. The point is, get out there. National Parks are your Open Country.