All collecting within National Park Service areas requires a permit, and these permits are only issued for scientific research with an approved research proposal. Research proposals must include a research design describing how a hypothesis will be tested and affiliation with a research institution.
Limited fossil collecting for non-commercial, personal use on some public lands is legal.
Specific areas may be posted, or designated, with different regulations. Before collecting, check with the local agency office to assure compliance. Check with the agency managing the land in question before collecting. NPS Lands - Requires a permit. BLM Lands - Requires a permit.