The 56-year-old comedian and actor arrived in Sweden just over a week ago to play a few rounds with his pro-golfer friend Jeff Sluman, according to the newspaper.
On Sunday evening, Murray hit the town with some golfers who had participated in the Scandinavian Masters tournament. When the evening's festivities at Café Opera drew to a close, he hopped into a golf cart and made a beeline for his hotel.
Soon however police asked the American actor to pull over when they suspected that he may have been driving the buggy while under the influence of alcohol.
But the star of films such as 'Ghostbusters', 'Lost in Translation' and golf comedy 'Caddyshack' refused to take a breath test and was taken to Norrmalm police station in the north of the city.
"Bill Murray refused to blow into the breathalyzer in town, making reference to American laws. He was then brought in to the police station but he still didn't want to blow into the breathalyzer.
"He was adamant that he wanted to take a blood test," police spokesman Christer Holmlund told Dagens Nyheter.
The officer, who described Murray as "very pleasant", added that he had never before come across a golf cart in the city centre during his thirty years in the force.
Murray was not formally arrested however and was permitted to leave the station after leaving a blood sample.
The results of the test will be ready in two weeks. Murray is understood by Dagens Nyheter to have given a police officer clearance to represent him during any future court proceedings.
An eyewitness spoke to Expressen about Murray's erratic behaviour.
"He was driving very, very slowly on the footpath along Birger Jarlsgatan. He took a break for a while at a Seven Eleven before driving on home to the Hotell Anglais."