The woman rang 999 after noticing the snowman outside her house had vanished.
"There's been a theft from outside my house," she told the operator. "I haven't been out to check on him for five hours but I went outside for a fag and he's gone."
When asked who had disappeared, the woman said: "my snowman." Chief inspector Simon Black said that the call "could have cost someone's life if there was a genuine emergency and they couldn't get through."
The woman told the operator: "I thought that with it being icy and there not being anybody about he'd be safe. It ain't a nice road but you don't expect anybody to nick your snowman."
Black said that they had spoken with the woman and warned her not to call unless she was in an emergency.
Even though abusing the emergency services system is a prosecutable offence in Britain, she will not be charged.
"In this case the woman genuinely thought this was a theft that she should report it because she'd used pound coins for the eyes and teaspoons for the arms," Black added.