Money and jewellery was taken from two cars while parked in Langholm, with both vehicles having been left unlocked.
A grey Hyundai I30 was left parked outside an address at Meikleholm Side reported at 6.30 pm on Saturday.
Sgt Steven Wilson from Annan Police Station said: “She said that the vehicle had been left unsecured for a period of time.
“And at 12.30 pm on May 2 she realised that a quantity of cash had been stolen from the vehicle and contacted the police.”
In a separate incident, on May 2, jewellery was stolen from an unsecured car while left in a parking bay outside the Blue Moon shop in Langholm’s High Street.
Sgt Wilson said: “It occurred between 10.45 am and 11 am on Monday. “The person reported that they’d popped into the shop for a brief period and left her white Fiat 500 in the parking bays outside.
“She later noticed that two pieces of jewellery had been taken from within the car – a silver necklace with a silver oval pendant and a black stone set in the pendant and a pair of silver earrings in an oval shape with a black stone set on one side.”
The driver said that her vehicle had been left secured at all other times.
Issuing a warning, Sgt Wilson said: “This was broad daylight, in the middle of a high street – we don’t often get reports like this.
“Obviously if anyone knows anything about either of these crimes or has seen anybody hanging around acting suspiciously at all, then please get in touch with either local officers or Police Scotland.”