When the woman went into her kitchen, the girls ran off empty-handed into St Giles Terrace, where they were lost to sight.

Detectives are investigating the “suspicious” incident involving the girls — who are described as being between 15 and 16 years old — which took place in the early hours of yesterday.

One of the girls is around 5’6”, of slim to medium build with long blonde hair tied up in a ponytail. She was wearing a red hooded top and dark tracksuit bottoms.

The other girl is described as around 5’2”, of slim build with shoulder-length brown hair. She was wearing a dark top and bottoms.

A spokeswoman for Tayside Police said, “It is highly likely that these two girls were in the property with the specific intent to steal.

“With the weather improving many people leave doors ajar and windows open to keep their homes cool. However, this is the perfect opportunity for sneak thieves.

“At night time, or if you are sleeping during the day, please make sure that your windows and doors are secured.’’

Anyone who can identify either of the girls described, or anyone who remembers seeing anyone acting suspiciously in the area, should get in touch with Tayside Police on 0300 111 2222.