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.

The annual Bank of Scotland Business Digital Index assessed small firms in five key skills needed to get the most out of being online.
It found that fewer than a third of small businesses north of the border lacked these basic skills.
This compares to a UK average of 38%. Only London rivals Scotland in terms of this measure.
Experts said the lack of key digital skills was a primary barrier to doing more business online, with 15% of firms across the UK stating this was the main barrier, more than doubling since 2015.
The skills assessed for the current report were managing information, communicating, transacting, creating and problem solving.
The report also noted cyber security was rising in prominence as a reason for small businesses not doing more online.
Almost 60% of Scottish firms said they still needed to invest in cyber security, lower than the UK average of 69%.
Philip Grant, chair of the bank's Scottish executive committee, said: "It's pleasing to see that the Business Digital Index shows digital maturity is increasing for small businesses in Scotland, however, there are still too many without basic digital skills.
"It's clear that being online can open the doors to opportunities, as well as cost and time saving benefits.
"We must do more to encourage small businesses based in Scotland to invest in digital skills, allowing them to make the most out of being online and to reap the benefits."
Two thousand businesses and charities across the UK were surveyed, including 109 in Scotland. The study was developed along with Doteveryone and Accenture.
An investigation into the disappearance of a woman who was allegedly murdered is to be probed by the police watchdog.
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Small businesses in Scotland are leading the way when it comes to digital skills, according to a study.