A German woman has hired a lawyer after being shocked to discover that not only did police deliberately run over her beloved dog, they have now sent her a hefty bill, it emerged on Monday.

Robby, a nine-year-old Australian Shepherd, ran away on 31 December after being terrified by fireworks, and made it onto a nearby motorway, her owner Heidi Schwank (65) told the Bild daily.

"A day after New Year's, the police phoned me and said that my Robby had been run over on the motorway.... The police claimed that a motorist had hit and killed Robby," said Schwank, photographed clutching his picture.

But it turned out that it was the police who had killed Robby after four officers in two police cars spent over an hour getting cars on the A1 autobahn near Hamburg to slow down while they tried, unsuccessfully, to capture him.

Neutralising Robby caused damage of over ?2500 ($3500) to a patrol car ? costs which Schwank now has to pay.

Contacted by AFP, a police spokesperson said that the officers "were confronted by something posing a danger, this 'wonderful dog' tearing about to and fro on both carriageways of a motorway." "At a time like this, a police officer has to weigh up the lives of people against that of a dog," spokesperson Jessica Wessel said.

"You can imagine that in the dark, on New Year's Eve with explosions and everything all around, a dog being chased by strangers is not going to calm down, and you're not going to catch him."

Schwank however is incensed.

"They close off motorways even for ducks. Why not for my Robby? Then they could have caught him safely ? and my beloved would still be alive," the pensioner told Bild.