Short answer, yes. Long answer, your concerns go deeper than Game and Parks.
Any one of about 50 + local, state and Fed gov agencies have the legal ability to detain, and arrest you, if circumstances warrant. Any one of those agencies, are the ones you need to fess up to about your CHP.
Add to that mix, any vehicle that has emergency lights on it, Police, fire, emergency, and the local Red Cross?? Or even The Seventh Day Adventists?? (ADRA) in case of a declared disaster.
Here are a few agencies at the Fed Gov level, that have investigative and arrest powers.
As Nebraska has federal land used as parks, and federal highways, you could come across some of the people in this list, here in Nebraska.
•U.S. Customs and Border Protection (36,863 officers)
•Federal Bureau of Prisons (16,835)
•Federal Bureau of Investigation (12,760)
•U.S. Immigration and Customs Enforcement (12,446)
•U.S. Secret Service (5,213)
•Administrative Office of the U.S. Courts (4,696)
•Drug Enforcement Administration (4,308)
•U.S. Marshals Service (3,313)
•Veterans Health Administration (3,128)
•Internal Revenue Service, Criminal Investigation (2,636)
•Bureau of Alcohol, Tobacco, Firearms and Explosives (2,541)
•U.S. Postal Inspection Service (2,288)
•U.S. Capitol Police (1,637)
•National Park Service - Rangers (1,404)
•Bureau of Diplomatic Security (1,049)
•Pentagon Force Protection Agency (725)
•U.S. Forest Service (644)
•U.S. Fish and Wildlife Service (598)
•National Park Service - U.S. Park Police (547)
•National Nuclear Security Administration (363)
•U.S. Mint Police (316)
•Amtrak Police (305)
•Bureau of Indian Affairs (277)
•Bureau of Land Management (255)
•Bureau of Engraving and Printing (207 officers)
•Environmental Protection Agency (202)
•Food and Drug Administration (183)
•National Oceanic and Atmospheric Administration (149)
•Tennessee Valley Authority (145)
•Federal Reserve Board (141)
•U.S. Supreme Court (139)
•Bureau of Industry and Security (103)
•National Institutes of Health (94)
•Library of Congress (85)*
•Federal Emergency Management Agency (84)
•National Aeronautics and Space Administration (62)
•Government Printing Office (41)
•National Institute of Standards & Technology (28)
•Smithsonian National Zoological Park (26)
•Bureau of Reclamation (21)
Here is a larger list, if you want to see how large Uncle Sam is.
http://en.wikipedia.org/wiki/Federal_law_enforcement_in_the_United_States