The situation seems pretty complicated. First, according to the NBC (March 5, 2019):
Vermont is one of a handful of states where voters do not register by party and can participate in any primary they wish, so Sanders has never had to officially declare his personal partisan membership.
Second, in 2015, in order to run in the Democratic primaries...
When Sanders ran for president in 2016, there was some question about whether he would qualify for the ballot in New Hampshire, home to the first-in-the-nation presidential primary, because state law requires candidates to be a member of the party they're seeking to represent in the general election.
The chairman of the state Democratic party personally accompanied Sanders to the secretary of state's office to vouch for him and make sure the candidate would get on the ballot.
Now as far as his Senate party identification:
"I am the longest-serving independent in the history of the United States Congress. That’s how the people of Vermont sent me to Washington and I'm proud of that," Sanders told reporters after filing for his paperwork in New Hampshire in late 2015. "And I had to make a decision six months ago. Do I run as a Democrat or do I run as an Independent? And I made that decision. I am running as a Democrat, obviously. I am a Democrat now."
A reporter followed up by asking if Sanders would run in all potential future elections as a Democrat and Sanders replied, "Yes."
Also according to the NPR (a story that ran a day before, i.e. on March 4, 2019), while Sanders is technically an independent Senator he
caucuses with the Democrats in the Senate.
And the same story said that Sanders had already registered to run as an independent Senator in 2024!
Bernie Sanders filed Monday to be a candidate for the Senate in 2024 — as an independent.
Also on March 6, 2019, CNN/NPR broadcast this exchange/commentary
KELLY: Just briefly, safe to say this is unusual to have a candidate running for Senate as an independent and for president as a Democrat at the same time.
MONTANARO: Yeah. I mean, I can't think of one who's done that in recent memory.