The body of India Chipchase, 20, a bar worker, was found in Northampton on Sunday.
Book-keeper Edward Tenniswood, 51, from Stanley Road, faces a charge of murder and has appeared at crown court.
Northamptonshire Police referred itself to the Independent Police Complaints Commission over its "responses before and during" the search.
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A statement issued by the force said: "Northamptonshire Police has made a referral to the Independent Police Complaints Commission to ensure transparency in examining police action and responses before and during the search for India Chipchase.
"We await the decision of the IPCC and will not be commenting further as the criminal investigation is now in the court process."
On Thursday Mr Tenniswood appeared at Northampton Crown Court via video link from Woodhill Prison in Milton Keynes.
When asked if he could hear, Mr Tenniswood told the clerk of the court: "I can hear you, definitely."
After that he spoke only to confirm he could see the Judge Rupert Mayo, prosecutor Mary Loram and his lawyer Derek Johashen.
There was no application for bail and he was remanded in custody.
Ms Chipchase was last seen by friends on Bridge Street at about 01:15 GMT on Saturday.
Her disappearance was reported later that day after she failed to turn up to work at The Collingtree pub and restaurant.
Her body was found at the defendant's terraced house in Stanley Road. A post-mortem examination concluded she died as a result of pressure to the neck.
There will be a plea hearing on the 25 May, and a trial date was set for 18 July, to last for 10 days.
An investigation into the disappearance of a woman who was allegedly murdered is to be probed by the police watchdog.