There have been 285 public insurance claims for injuries caused by electric scooters since US-based Lime E Scooters launched in Auckland and Christchurch in October.

This included 171 Accident Compensation Corporation claims in Auckland between October 14 and November 25 and 102 in Christchurch - the two cities where Lime has launched its services.

Over the same period across the rest of New Zealand, there were just 12 claims for e-scooter-related injuries.

The data also shows the rate of injuries has been accelerating.

In the first month after Lime's launch - between October 14 and November 12 - there were nearly 150 injury claims.

But since then almost been as many claims have been made, with around 135 laid in the last 13 days.

The latest injury statistics come as Lime scooters continue to show up in unusual places.

Two have been found in Marlborough recently - one in Blenheim and one in Picton - despite the scooters only being officially available for use hundreds of kilometres away in Christchurch, media outlet Stuff reports.

The Lime Scooters were now being held in the Blenheim police station with the news following on from media reports another rusty scooter had washed up on an Auckland beach earlier this month with barnacles on it.

New Zealand police have also been pictured with Lime Scooters in Auckland after an officer on a late-night shift in the city centre recently took one for a joyride.

Footage posted to social media shows a group of officers talking to two men outside the Mobil and KFC in Quay St before one officer goes for a spin on one around the carpark.

Lime is also understood to be considering rolling out its scooters on Wellington's streets.

Wellington City Council confirmed earlier this month several companies - including Lime - had approached the council about introducing electric scooters to the capital.

Council transport portfolio leader Chris Calvi-Freeman said his team were taking a cautious approach.

The scooters were fairly harmless when used carefully but there would always be a minority of situations where there could be conflict, he said.

"They can be used at up to 27km/h on the footpath. Now that's a crazy situation so we have to be very careful about what we're promoting," he said.

In Auckland, customers also went wild when Chinese electronics giant Xiaomi, or "Mi" as many know it, opened its first store offering electric scooters for private use.

The Mt Wellington store reportedly sold $257,750 worth of electric scooters in its first seven hours after customers had earlier queued to get inside.