Two men have been arrested after one allegedly broke into the South Australian Supreme Court and the other a major Adelaide police station on the same night.

Key points: A man has handed himself in for allegedly breaking into the Supreme Court

A man has handed himself in for allegedly breaking into the Supreme Court Police are yet to work out what was stolen from the building

Police are yet to work out what was stolen from the building A man has also been arrested for allegedly breaking into the Sturt police station

Police have not worked out what was stolen from the Gouger Street court building, while items allegedly taken from the Sturt police station were recovered.

Police said a 27-year-old man of no fixed address climbed a wall on the western side of the court and entered through a rear door about 11:45pm on Friday night.

He moved through a number of offices and public areas before leaving.

He was charged with serious criminal trespass and theft on Saturday night after handing himself in.

He has been refused bail to appear in the Adelaide Magistrates Court — opposite the Supreme Court on Victoria Square — tomorrow.

Police said they were "yet to determine" what was taken from the building, which is undergoing a $31 million renovation and expansion.

Man arrested after police station break-in

Separately, a man was arrested for allegedly breaking into the Sturt police station, on Sturt Road, about 8:15am on Saturday.

The Sturt police station has been closed since July. ( ABC News: Claire Campbell )

Police said they spotted a 27-year-old man from North Plympton walking away from a restricted area of the station.

An officer tried to stop him to speak to him but he ran away.

Police later arrested him in Bradley Grove and detained him under the Mental Health Act.

Officers said they discovered a glass door at the back of the station had been smashed with a rock.

Items that were allegedly stolen have now been found.

"There was no operational equipment or confidential documents on site or stolen," police said in a statement.

The police station is closed while the cause of cracks in walls is investigated.