A farmer has warned that the meat of 16 lambs stolen over the weekend could be poisonous if eaten.
PSNI has asked staff at abattoirs to be vigilant for the missing flock.
Chief Inspector Graham Dodds said: "The farmer who owned these lambs has informed us that they would not be ready to enter the food chain for the next six weeks and that their meat would be poisonous to humans if eaten.
"I would therefore ask any abattoirs to be aware of this and carry out the proper checks on any lambs that they come into contact with in the next few weeks."
The 16 lambs were taken from the farm on the Eglish Road, Dungannon, on Saturday evening. Police received the report of the theft just after 8.30pm.
Stringent EU regulations mean that animals which have been vaccinated or treated with antibiotics have to be kept out of the food chain for six weeks. It is thought that the stolen lambs may have recently been vaccinated.
Ulster Farmers' Union (UFU) President Ian Marshall stressed that the incident would cause little risk to consumers and therefore should not be of concern to the public. He said: "Unfortunately, the theft of livestock is something we see far too often and it can be very stressful for the farmer involved. We are concerned that the rural crime statistics are still alarming in this part of the world and it's a level that we do not seem to be getting on top of."
Despite the drop in current lamb prices, the animals are estimated to be worth between £800 and £900 in total.
According to the UFU, in 2013, rural crime was up 15% from 2012 and was estimated to cost farmers £3.9m. Livestock, tractors, and tools were the most common items to be targeted.
Meanwhile, a major cross-border hunt is continuing for a gang of sheep rustlers who snatched 40 sheep from a farm in Co Monaghan, close to the south Armagh border.