Many undertakers across Dumfries and Galloway say the system operated by the former regional force worked well.
Previously arrangements were made with undertakers in each district to deal with accidents and other fatalities.
Now, following the merger of forces, a review of the supply of all goods and services to Police Scotland is underway, including the transportation of deceased persons.
Kenny Bell, of HK Thorburn of Lochmaben, says his firm could not operate regionwide.
He said: “There is a rota system in operation at the moment in Annandale and Eskdale which seems to work. I don’t know if plans to change it would work for Dumfries and Galloway is a very big region and we could never undertake anything like that.”
He added: “My business is not big and I tend to look after our own settlement and the surrounding area.
“From my point of view it is all about families and the first call is very important. It might be different in the Central Belt, but here we know most of the people in the area.”
Another local funeral director said: “Many families in this area know and trust their local funeral directors and want a personal touch.
“This new regulation is both taking away choice as well as causing damage to local businesses. It’s bad enough that families have to deal with the sudden death of a loved one without having to be told who to turn to and having all choice taken from them.”
Dignity Funerals, which owns John Pagan of Dumfries, Kenneth Henderson of Annan and V and M Thomson of Lockerbie, said that prior to the formation of Police Scotland, they held contracts with Strathclyde Police and Lothian and Borders Police.
Spokesman Stuart Cox added: “These contracts have been extended until Police Scotland make an appointment but invitation to tender has not yet been made.”
Police Scotland held information sessions in Aberdeen, Inverness, Glasgow and Edinburgh in January about the procurement process and service requirements.
And a statement from Police Scotland said: “The Police will ensure a fair, open and transparent process is used to award business in line with legislative requirements.
“The public will receive a standard of service which will be monitored, and contract managed, to ensure an equitable service is implemented across the country in support of bereaved families in such difficult times.”