Yes, but it still would have to go before Congress. Article IV, Section 3, Clause 1:
"New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress."
At initial thought, that does not seem to have any bearing if a portion of a state wishes to secede from the state. That portion just will not be a part of the USA.
It is likely that the last census will be used to re-allocate the representative districts due to the population loss and resultant loss of representation in Congress.
Having said that, there will have to be some type of way to account for federal ownership of lands and other items within the boundaries of that portion, so it might be a tough thing for that portion to actually accomplish. There will have to be some way to allocate debt the US assumed while that portion was part of the US.
Bottomline: Tough