From the Super Mario Wiki
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Star Doors have appeared in Super Mario 64 and its remake Super Mario 64 DS inside Peach's Castle. Like most locked doors in these games, a certain number of Power Stars must be obtained before they can be opened (although Star Doors require many more Power Stars than regular doors). Once unlocked, the doors will slide open allowing Mario to enter. No other character may open a Star Door. However once they're open, anyone can enter them.
Four star doors exist in the games: