The force said the new approach would allow local teams to focus on patrols, and issues like anti-social behaviour.
A spokesperson confirmed most investigations would be dealt with by a "default" team, but said that did not rule out local officers being involved.
Critics have raised concerns that fewer officers will be investigating crimes.
The changes are part of Leicestershire Police's bid to reduce spending by Â£30m.
Under the plans, the force is also reducing the number of local units from 15 to eight and will cut 300 of its 2,200 officer posts over the next two years.
Beat officers will now be known as dedicated neighbourhood officers to reflect the changes, which came into effect earlier, bosses said.
Half of the 68 officers in the new East County team, which includes Rutland, Melton and Harborough area, will be PCSOs.
Shadow policing minister Jack Dromey said the public should be concerned about the changes.
He said: "Because there will be far fewer officers investigating crime - more criminals are going to get away with it."
Rutland County Council leader Roger Begy said he feared the changes would also lead to longer response times.
"We are a very low crime area [in Rutland] but we want to keep it that way," he said.
However, Chief Constable Simon Cole said the force was "putting officers where the problems are".
"This transformation is the latest in a series of on-going changes in response to reducing budgets and changing public expectation and demand," he said.
"This new way of working will allow the teams based in our communities to dedicate their time to working closely with neighbourhoods and partners to resolve issues at a local level."
Police investigations in Leicestershire are being carried out by a dedicated unit rather than beat officers, as part of changes to working practices.