Officers have less than 12 hours to either prosecute or release a man arrested in connection with the disappearance of Libby Squire.
The investigation into the disappearance of 21-year-old Libby is now on the tenth day after the University of Hull student disappeared on Thursday, January 31.
Police were granted an extension to question their 24-year-old male suspect. However, she only has until 21:11 to decide whether to accuse or dismiss him.
Alternatively, officers may request another extension to continue the interview.
Detective Superintendent Mathew Hutchinson said, "I can confirm that the court granted us another 24 hours to question the man.
"We still consider Libby's disappearance as an investigation of a missing person.
"I have already said that we remain open about her whereabouts, and that is still the case.
"Our top priority is to find Libby Squire, and we're still doing extensive searches and getting all the information out to the public."
Libby was seen in a taxi at around 11pm on Thursday, January 31, near Welly on Beverley Road in Hull, Hull Live reports.
She was dropped off outside her Wellesley Avenue home, but did not enter.
The University of Hull student was later seen at around 11:45 pm on the street near the intersection with Beresford Avenue, when a man got out of his car to stop and help her.
CCTV then caught her on a bench near a bus stop on Haworth Street, where officials believe she was at 12:09.
She has not been seen since.
The police launched a massive search on Friday, February 1, when dozens of officers fought the area around Beverley Road, Wellesley Avenue, Haworth Street, and Barmston Drain.
The Humberside Police Major Crime team, based in North Lincolnshire, was drafted into the North Bank earlier this week to help investigate their disappearance.
If anyone has information about the investigation, call the Humberside Police 101 emergency number.