Rian Christopher Minnis, 28, was arrested after an alleged pursuit through Griffith on Tuesday afternoon. He is accused of accelerating rapidly past a police vehicle in a white Toyota Corolla and ignoring police when they tried to stop him.

Officers allegedly chased Minnis through several Griffith streets before calling the pursuit off. Police saw him walking along Captain Cook Crescent and arrested him.

The 28-year-old faced the ACT Magistrates Court on Wednesday and applied for bail.

A police officer told the court Minnis was ''couch surfing'' and that there were concerns over an address in Richardson he had provided to authorities. At one point, the prosecution alerted the court that the address may not exist. The police officer and Minnis' lawyer checked their mobile devices in the courtroom, until the defence found the address for the court.

The prosecution opposed bail on fears that Minnis may reoffend and that he could collude to fabricate evidence with others who were in the car.

Police were still investigating whether the Hertz rental car had been stolen.

Minnis had made no admissions to the alleged pursuit, the court heard. The defendant only had one conviction but is facing a series of matters in ACT courts.

Chief Magistrate Lorraine Walker said it appeared as though the spate of alleged crimes may have been sparked by drug use.

Ms Walker bailed Minnis on strict conditions, including that he reside as directed by authorities and that he submit to drug and alcohol monitoring. He is also banned from driving or having car keys.