North Yorkshire Police have released a 59-year-old man on conditional bail following his arrest on Tuesday (May 13) on suspicion of murdering Claudia Lawrence.
The man was named locally as Michael Snelling.
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,” the police said in a statement.
“North Yorkshire Police would like to thank those people for their patience and understanding.”
Meanwhile the force has warned the media to take care in its reporting of the investigation.
“As investigations continue with the possibility of further arrests to be made, all sections of the community and the media are reminded and encouraged to respect the rights of others, including those connected to the case,” the police statement said.
“It is also important that the investigation team have every opportunity to follow due legal process.”
The force drew attention to a statement it issued earlier about responsible reporting in line with the Contempt of Court Act, “and the fact, to date, nobody has been charged with any criminal act emanating from this case”.