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The blaze occurred at a house in Hurworth Street at around 7pm on Wednesday, the force said.
No-one was inside the property at the time of the incident, but the potential for injury was ``very real'', according to DC Phil Henderson of Hartlepool Police.
He said: ``The house was unoccupied at the time so there were no casualties; however, we believe the fire was started deliberately and the potential for serious injury was very real. This incident could have been a lot worse.''
The fire caused substantial damage to the house after items were set on fire intentionally, according to the force.
Dc Henderson is now appealing for anyone who may have witnessed the blaze or seen anything suspicious to contact Cleveland Police on 01642 302138 or alternatively, contact Crimestoppers on 0800 555 111.