The warning comes as two people, who made allegations that later turned out to be untrue, were given £80 fines during February.
A 26-year-old man from Bruce Crescent, Hartlepool, was fined after claiming a television set had been stolen in a burglary - only for police to find it in an upstairs bedroom.
Also last month, a 19-year-old woman from Hurworth Street, Hartlepool, falsely reported she had been assaulted by an ex-partner.
Detective Inspector Keith Groves of Hartlepool Police said: "Inquiries revealed the TV was actually upstairs in the house and he was fined £80 for wasting police time.
"We will continue to scrutinise each and every crime reported to us and people making false allegations will be dealt with appropriately."
Crime in Hartlepool has dropped to manageable levels where every incident reported is fully investigated, flagging up things that might have gone unnoticed previously.
Police have the power to hand out the fixed penalty fines for wasting police time without having to go through the court system.
Other false crimes police have punished in recent months include reports of a stolen car, mobile phone thefts and burglaries.
Police say false reports pull officers away from investigating real crimes. Motives behind false allegations are said to include revenge and financial gain by cashing in on insurance claims.
Det Insp Groves added: "In the cold light of day when they are faced with a police officer they admit it.
"But by then we have put a lot of resources into investigating allegations and we have to deal with them appropriately.