Some Oamaru residents continue to flout the nationwide Covid-19 lockdown, a stance that has raised the ire of police.

In two separate incidents, an Oamaru man known to police allegedly went to a Thames Highway address about 10pm on Wednesday and confronted another person, before punching them.

That followed an earlier report of a person who had previously been served a trespass notice forbidding them to enter a McLean St address being discovered at the north Oamaru property.

Inquiries are continuing into both incidents.

Senior Sergeant Jason McCoy, of Oamaru, said they were of particular concern given the current climate, as those involved put everyone at risk.

''We have got covid going on. What are these people doing?

''It's not ideal. We are not encouraging that movement at all. We really want people to be staying in lockdown and in their bubble. We don't want them going 30km down the Alps 2 Ocean trail, we don't want them going to the beach.

''We don't really want people from the South Hill area going to the North End of Oamaru . . . they should be keeping in their own little suburb. We are disappointed people are breaching that.''

His plea comes just days after he echoed the words of Prime Minister Jacinda Ardern, who has urged residents to ''be kind'' amid the lockdown.

Meanwhile, a man sustained minor injuries after his vehicle left State Highway 1 near Maheno south of Oamaru between 1am and 2am yesterday.

Snr Sgt McCoy said the driver and sole occupant failed to negotiate a slight bend.

Alcohol may have been a factor in the crash, he said.

The man was taken to Oamaru Hospital via ambulance.

Inquiries are continuing.

daniel.birchfield@odt.co.nz