Sergeant Warren Mitchell said Badu was charged after a witness offered a sworn statement to police on Thursday.
Badu's spokeswoman had no immediate comment on Friday.
The singer, who was born in Dallas, performed a walking striptease in front of tourists and pedestrians during the shoot in Dealey Plaza on 13 March for her video for the song Window Seat.
I’m sure Sergeant Warren is proud of his gallant effort to protect the innocent eyes of our children. Check out the video. Of course, her video will be on MTV for the next 10 years so I’m not sure what good fining her does.