Which new england state refused to join the united states after the revolutionary war and declared itself an independent country with its own president, money and postal service?

Vermont

Originally known as "New Connecticut," a convention of those wanting to separate themselves from both Great Britain and New York met to remove themselves from the war and establish their own governance.  Historians refer to the "Vermont Republic" existing from 1777 to 1791.  The state of Vermont was admitted to the Union in 1791.