Not really. The state does not lose jurisdiction merely because a crime was committed in a national forest. See US Code 16-480:
16 U.S. Code § 480. Civil and criminal jurisdiction
The jurisdiction, both civil and criminal, over
persons within national forests shall not be affected or changed by reason of their existence, except so far as the punishment of offenses against the United States therein is concerned; the intent and meaning of this provision being that
the State wherein any such national forest is situated shall not, by reason of the establishment thereof, lose its jurisdiction, nor the inhabitants thereof their rights and privileges as citizens, or be absolved from their duties as citizens of the State.
(June 4, 1897, ch. 2, § 1,
30 Stat. 36; Mar. 1, 1911, ch. 186, § 12,
36 Stat. 963.)
16 U.S. Code § 480 - Civil and criminal jurisdiction