A report of someone using an e-scooter to pull a trailer at 60mph is one of 120 reports of offences involving the vehicles in the past year.
Norfolk Constabulary provided information of the 120 reports following a freedom of information request.
Reports included "suspects on electric scooters" when involved in other crimes such as burglaries and assaults.
E-scooters were also involved in a report of someone who "made off from police."
One recent report in Belton involved a teacher, John Sanders, receiving two fractures to his eye socket in a hit and run collision with an e-scooter rider.
The rider's identity is still unknown.
Following the incident, Mr Sanders, 54, said: "There has to be some social responsibility."
Mr Sanders is currently a supply teacher and is unable to work due to his injuries. He says this has caused a financial issue for him and his family.
"I think there just has to be better safety aspects about e-scooters, insurance wise, noise wise," he said.
"To me, they can’t share pathways with pedestrians. Anything motorised shouldn’t be on the pavement."
Norfolk Police revealed a number of traffic offences among the incidents, including drink driving and an e-scooter driving at 60mph while pulling a trailer.
Temporary Chief Inspector Jon Chapman, head of the Joint Roads and Armed Policing Team, said: “E-scooters are classed as a motor vehicle under the Road Traffic Act and therefore we must remind users to treat them as such.
“As it is a motor vehicle, the Road Traffic Act also provides powers to police to stop users of e-scooters for offences such as drug and drink driving as well as careless or dangerous driving.
"It is important that users stick to the roads. The use of e-scooters on pavements is not allowed by law."
He stressed that the use of regular electric scooters was illegal when driven anywhere other than private land.
In Great Yarmouth, trials for the Ginger e-scooter hire service began on Tuesday, March 30.
Great Yarmouth Borough councillor Penny Carpenter, who tested a Ginger e-scooter around the time the trial launched, said: "This is very much a trial – we will learn lessons as we go, welcome constructive feedback and will work with Ginger to review operations.”
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