https://www.sec.state.vt.us/media/406433/ElectionLawBook12-11.pdf
Paragraph 2702 of the PDF covers nominating petitions.
Vermont is not like New Hampshire, as they do not require the Candidate to be a member of the party in which he or she intends to run.
However, there are whole sections on the political parties, how they are organized, and what party they play in law and elections.
It specifically states that no person can vote for more than one party in a primary. People choose a party, and in Presidential Primary years, that party is recorded.
Dean, throughout his career as a politician affiliated with Democratic Party, as has Senator Leahy.
Democrats have tended to control the state since Kennedy. Before that, Vermont was a Republican Stronghold.
The argument about people not registering for parties is irrelevant. The Parties in Vermont know which elected officials are Democrats, Republicans, Progressives, or Independents. Sanders chose not to belong to the Democratic Party.
Now, if you read the article I posted, it states that Bernie will do what it takes to run in all 50 states. I suspect he will officially affiliate in the Democratic Party in states where it is required.
He is an intelligent man with a team that will figure out what is necessary.