Officers in Hull have stopped investigating less serious crime, the city's police commander said.
Instead, they will prioritise the more serious offences in a bid to clear a backlog of 3,500 cases and meet Home Office targets before the end of March.
Unless there is an obvious suspect, less serious crimes such as theft and criminal damage will not be investigated, Ch Supt Sean White said.
He said it was a short-term measure in a city with about 130 crimes each day.
"For a period between mid-December last year and next Sunday, 2 April , we have been focusing our resources on clearing a backlog of more serious offences like violent crimes, robberies, burglaries and vehicle crime," he said.
"I understand the public concern but I want to make it clear we will still arrest people"
"But if there's no obvious suspect and it's going to require further inquiries, and maybe a prolonged investigation, then we're leaving it on file.
"We've built up a backlog of some 3,500 more serious crimes which needs to be tackled. We thought we ought to prioritise those."
He said his division needed to match its resources to its workload and was also trying to meet Home Office targets, set by the Police Standards Committee, to reduce the backlog of crimes by 31 March.
"I understand the public concern but I want to make it clear we will still arrest people," he said.
"We will only let the crime lie on file where there needs to be a protracted investigation."
Police will only investigate if a prolific offender is involved, the victim is vulnerable, such as the elderly or disabled, or the crime is categorised as racist or homophobic, he said.
A Humberside Police spokesman emphasised it was a short-term policy that applied to the Hull area only.
Under a plan recommended on Tuesday by the Home Secretary, the Humberside force would merge with the three Yorkshire forces to form the largest force in area in the country.
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