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.

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

"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," Ms Schwank said, 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 ($3907) to a patrol car, costs which Ms Schwank now has to pay.

A police spokeswoman said that the officers "were confronted by something posing a danger, this 'wonderful dog' tearing about to and fro on both lane of a highway."

"At a time like this, a police officer has to weigh up the lives of people against that of a dog," spokeswoman 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."

Ms 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 retiree said.