Some minor crimes will no longer be investigated as part of a project being piloted in the north east of Scotland.
Police Scotland said it wants to give officers more time to focus on responding to emergencies and keeping people safe from harm.
An example of where no further action may be taken was a garden theft with no CCTV or eye-witness evidence.
Police Scotland said: “Hard choices are being made to deliver effective policing within the funding available.
The new pilot has been described as a “proportionate response to crime”.
It comes days after UK Home Secretary Suella Braverman said the police in England and Wales must investigate every theft and follow all reasonable leads to catch offenders.
Ms Braverman said it was “completely unacceptable” that criminals are often “effectively free to break certain laws”.
Police Scotland said that currently members of the public may have to wait some time to hear whether their report of a crime is being investigated.
However, under the new approach the aim is to inform people of the decision more quickly.
Divisional commander Ch Supt Graeme Mackie said: “The pilot process will enable local police officers to focus on those crimes that have proportionate lines of inquiry and potentially enable them to give more time to local concerns and priorities in the area.
“We also know that sometimes people simply want to report a crime and we want to provide that service efficiently.”
He added: “Please continue to report crime in your area.
“Local officers will continue to review closed reports to enable them to map local crime trends and this may mean an inquiry is reopened and investigated.
Scottish Police Federation chairman David Threadgold told BBC Radio’s Good Morning Scotland programme: “I do not believe that any police officer in Scotland wishes to provide a poorer service than we are already being forced to do so.
“It is quite enlightening that the service is now being honest with the public of what it potentially will not be able to do in the future as a result of reductions in numbers and budget cuts.
“But I think for a national police force to say to its citizens that it potentially will no longer investigate certain crimes sets a dangerous precedent and we should be very careful.”
When asked if the force was delivering effective policing, he said: “The simple answer is no.”
He also raised concerns around intelligent criminals targeting specific areas and groups “safe in the knowledge that there will be no investigation on the back of their crimes”.
Mr Threadgold said: “We’re potentially going to withdraw a service from some of the most vulnerable members of our community while we continue to carry out functions which have got nothing to do with the police.
“If bold decisions are made about the way that we police mental health, some missing persons, patient transport, other functions that police are left with because there is no capacity with other public sectors, then we will create capacity that we need to provide services to the community.”
Scottish Conservative justice spokesman Russell Findlay MSP said the pilot was a result of “depleted policing” across Scotland.
“Police Scotland should be applauded for being so candid about the reality of their predicament, but communities deserve better than the SNP’s weak approach to justice,” he said.
“Ministers must be upfront with the public about whether this policy will potentially be rolled out elsewhere in Scotland.
“Police Scotland is being forced to make these impossible choices because the SNP government inflicted savage budget cuts while refusing to listen to warnings about the impact this would have.”
Scottish Liberal Democrat justice spokesperson, Liam McArthur MSP, said: “The police are being forced to make terrible choices because the Scottish government have expected them to do so much with so little for so long.
“The SNP’s botched centralisation of policing and brutal cuts have hit officer and staff numbers hard.”
The Scottish government said in a statement: “While these decisions are a matter for the Chief Constable, it is vital Police Scotland continues to inspire public trust and maintains relationships with local communities.
“This will be crucial when the results of this pilot are examined to ensure local priorities continue to be met with no detriment to communities.
“The Scottish government has increased police funding year-on-year since 2016-17, investing more than £11.6bn since the creation of Police Scotland in 2013, despite difficult financial circumstances due to UK Government austerity.”