A police spokeswoman said officers were called to reports of a man making threatening comments at Work and Income in Princes St about 12.30pm yesterday.
Police attended to trespass the man and a chase ensued, with the man heading in the direction of lower Stuart St on a skateboard.
The man (44) was arrested about 1.05pm and was being held in police custody. He is due to appear in court today on five charges.
Police said the charges were threatening to kill or cause grievous bodily harm, unlawful intimidation or threats, resisting police, disorderly behaviour and an indecent act with intent to insult.
Police were also called to the same office yesterday as the man was behaving in a similar manner, although officers were unable to locate him, the spokeswoman said.
A witness said he was at the traffic lights at the intersection of lower Stuart St and Moray Pl when he saw the man "flying down through the lights" heading towards the train station.
Two "puffed-as" constables were following behind the man.
The witness went to First Church and heard "tonnes of sirens" around the city.
He thought the man had been caught, but police cars kept coming past looking for the man.
Eventually police "swarmed" the church and dragged the man out.
Several officers were required to get the shouting man into the police car, the witness said.
"He was definitely not wanting to be in the situation he was," the witness said.