Prosecutors say that on September 21 last year, at the facility in Tom McDonald Avenue, Dundee, he sexually assaulted a woman, who cannot be named for legal reasons.
Stewart, 21, of Balmoral Gardens, Dundee, made no plea during a brief appearance at Dundee Sheriff Court before Sheriff John Rafferty
The case was continued for further examination and he was released on bail meantime.
A BBC documentary, titled Breaking Point, was broadcast on Monday making a string of allegations against staff at the unit – in the grounds of Ninewells Hospital – and featuring experts calling on it to be shut down.
NHS Tayside said it would investigate the claims in full and “will act”.
Last week a fatal accident inquiry into the death of Dale Thomson found there were “serious systemic failures” in the care he received at Carseview in the weeks before his suicide.