Police were called to investigate the disappearance of Daisy, a female Maltese Terrier, who was stolen from an after-hours drop-off cage at the RSPCA after 10pm on Sunday.

Daisy's distraught owners lost her twice on Sunday. The dog had been taken to the Weston facility on Sunday afternoon after a Good Samaritan discovered her lost in Monash. Daisy's owners went to collect her but shelter staff told them that an unknown dog-napper had cut into the enclosure and stolen the pint-sized dog.

Helen Puckett said Daisy had been part of her family for six years. The Stirling mother of two said the theft had distressed her family.

''It's very much a rollercoaster of emotions,'' she said. ''One minute she was safe and secure after searching for a number of hours and then we find that she's been taken.''

She said the pet of her 12-year-old daughter Elissa, would be of no value to breeders. ''She's desexed, she's microchipped. We've done everything we can to try to protect her, but she's just such a friendly dog that she'd go to anybody,'' she said.

RSPCA ACT chief executive Michael Linke said it wasn't the first case of dog-napping he had seen.

''It has happened before, but it's not common,'' he said. ''Sometimes it's people seeing their own dog and breaking in. Sometimes it's someone scouting for a free dog.''

The after-hours drop-off facility is equipped with heavy duty padlocks and takes up to 50 animals a week.

Mr Linke said cages were specially built five years ago with the intent to curb the then-higher theft rate. ''You're not going to walk past and break into them now. You've got to come with the right tools ... It's not your usual smash and grab,'' he said.

Mr Linke said they would boost security with the installation of night vision video surveillance.

However, he said an amnesty period was on offer to the thief. ''If they want to return the dog and just drop it in anonymously, no questions asked, we're quite happy with that.''

Police are asking for anyone with information about the theft to contact Crime Stoppers on 1800 333 000 or via www.act.crimestoppers.com.au

This reporter is on Twitter: @stephanieando