A Brisbane woman who allegedly set one police vehicle alight and tried to torch a second is in police custody in hospital.

Cassie Osterholm is further accused of attacking officers at Dutton Park Police Station following her arrest on Wednesday afternoon.

The 31-year-old - who has been charged with vehicle arson, attempted vehicle arson, trespass and two counts of serious assault of police - suffers from paranoid schizophrenia and needed urgent treatment, Brisbane Magistrates Court heard on Thursday.

She was taken to hospital in custody after briefly appearing on Thursday morning, having spent the night in the watch house.

She was charged after allegedly setting a police car on fire at Coorparoo station on Wednesday morning.

About 90 minutes before, she had poured fuel on the ground near another police vehicle at Carina station but fled on foot, police allege.

She was arrested about lunchtime and taken into custody.

"It will be further alleged that she assaulted officers once she was taken back to Dutton Park police station," police said.

Outside court, her sister Jade said Osterholm had suffered from early onset paranoid schizophrenia and had been unwell since she was 14.

Osterholm's mother Desley said she didn't sleep after learning of her daughter's arrest when she saw it on television news on Wednesday evening.

Osterholm is due back at court in June.