Dickens was forced to pull over after three of her tires were flattened by spike strips deployed by police, KPRC reported.
She was arrested on a charge of felony evading arrest, authorities said.
Harris County Sheriff's deputies said Dickens spit on several of them during the booking process and was "extremely combative," KHOU reported. Deputies said they had to put a spit guard over Dickens' mouth and hold her head in order to take a police mug shot, the television station reported.
Dickens' mother told KTRK the incident does not describe who her daughter is.
"She's not a criminal. She's just going through some stuff," Carmella Walker told the television station.