Northamptonshire's top cop warned he could order road blocks to force non-essential drivers off the road during the Covid-19 lockdown.
Some UK forces have already started stopping vehicles to check if journeys are necessary.
Chief Constable Nick Adderley said: "We are not at that stage yet.
"We will not be conducting road blocks at this stage but please support us and only make necessary journeys. I do not want to introduce road blocks but if people do not follow the Covid-19 instructions, I may have to.
"Key workers have contacted me worrying about being stopped by the police as they commute to and from work. I will be writing guidance and protocols for all my staff to ensure that a sensible and proportionate approach to roads policing is adopted."
Sunday's latest official figures show 19,522 confirmed cases of Covid-19 in the UK — 126 of them in Northamptonshire — with 1,228 deaths among people who tested positive for the bug.
A week ago, Prime Minister Boris Johnson ordered the nation to stay at home to stop the spread of coronavirus and said people who are not key workers should only exercise outdoors once a day or go out to do essential shopping in a bid to slow the spread of coronavirus.
Since then, some Northamptonshire folk have inundated police switchboards with 999 calls reporting neighbours who have gone for two runs a day instead of one, or who are having gatherings in their back garden and demanding they are arrested.
Other questions posed to operators have included whether it is illegal not to cough into a tissue.
Mr Adderley is launching a huge communications operation to keep the public informed of what they can and cannot do but will arm officers with strict instructions to issue sactions, penalties or arrest those who do not stick by the Government's directive to stay at home whenever possible.
He will take part in a Facebook live event tomorrow (Tuesday April 1) attempting to answer as many questions and concerns as he can.
Mr Adderley added: "Northamptonshire Police will enforce the law and issues sanctions, penalties or arrest those who do not follow the instructions given by the Government.
"But we very much want to ensure that sensible dialogue, common sense and co-operation is sought first.
"This is an opportunity for the public to unite, to come together with a common purpose of saving lives, protecting the NHS and making our county as safe as it can be. Together we will crack this!"
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