It happened around 11:00 Friday night near the intersection of West 4th and North Orange streets.
Two officers on patrol reported seeing 21-year-old Kasha Allen driving a black Chrysler 200 down West 4th Street.
Police say Allen suddenly crossed the double yellow lines nearly striking them.
The officers tried to pull Allen over but say she continued for about four more blocks before pulling over.
After seeing a round of ammunition in plain view, police ordered Allen out of the vehicle but she refused.
Authorities say Allen had to be physically removed.
Police were able to search the car and found an automatic handgun and 1.2 grams of marijuana.
Allen was taken into custody and faces various drug and weapon charges.