Police officers in Devon and Cornwall will no longer be routinely sent to all calls from the public, as part of cost-cutting changes.
Instead, only emergencies will receive an immediate response.
The force says a number of calls such as those about noisy neighbours are not policing matters and could be dealt with by councils or other agencies.
The force, which is cutting £47m over the next four years, says redirecting such calls will free up resources.
Chief Constable Stephen Otter told BBC News it was the biggest change in the force "since the Second World War".
He said: "It's a very significant change for us.
"We cannot just slice off costs from various units. We have to fundamentally change the way we work."
Serious crime calls would get a response from a CID officer, whereas minor crime such as bicycle thefts might be dealt with over the phone or by appointment at the local police station.
"We want to maintain the level of service that the public get at less cost," he said.
It was not "just about cutting costs, but also about thinking of better ways of doing things".
Nigel Rabbits of the Police Federation, which represents officers, said members were concerned about the changes.
He said: "It's very much dependent on driving down demand and my members have yet to see how that demand will be driven down."
A police spokesman said the changes would take place in agreement with local authorities and other agencies.
There would also be a publicity campaign.
Devon and Cornwall Police has to cut its budget by £47m over the next four years. It could result in 700 officer and 500 civilian support posts being lost.