Michael Snelling, 59, was arrested by officers yesterday morning.
A spokesman for the force said: "North Yorkshire Police have released a 59-year-old man on conditional bail following his arrest yesterday on suspicion of murdering Claudia Lawrence.
"Forensic searches at relevant properties are expected to continue for a number of days.
"Every effort will be made to minimise disruption to local residents and the public affected by this work.
"North Yorkshire Police would like to thank those people for their patience and understanding."
Forensic experts spent most of yesterday at the Burnholme Grove home of Mr Snelling and returned to the scene today.
Police Crime Scene Investigation teams have arrived at the house and a blue forensic tent has been erected over a paved area at the rear of the property.
Police officers carrying a forensic tent at the home of Michael Snelling in Burnholme Grove today. Picture: York Press
Police have also been searching a house in North Shields, where it is believed a relative of Mr Snelling lives.
Mr Snelling is believed to have worked for a mental health charity in York and, according to local residents, is an avid follower of Newcastle United.
A car has also been seized as part of the enquiries.
Detectives said yesterday they would like to stress that Ms Lawrence's body had not been found.
Police said they could not rule out the possibility of further arrests in the future.