Tagesspiegel reported on Tuesday that the marsupial had been spotted by a patrol car and briefly trapped on an industrial site, but escaped once again before its owners arrived to collect it.
Now police have decided that since the animal poses no danger, there will be no further search operations by police or their colleagues at the civil protection office (Ordnungsamt).
The kangaroo escaped at the end of November from its owner in Werder, near Potsdam, leading police, Ordnungsamt and passing drivers a merry dance before disappearing into the countryside.
Ordnungsamt officers in Werder told the newspaper that it was now the owner's responsibility to get it back.
Vets in Brandenburg said that the kangaroo should be able to survive winter away from shelter, with the primary danger to a marsupial on the loose being a road accident.
They added that without enough people armed with tranquilizer guns it would be difficult to catch him again.