They are alleged to have shouted abuse at staff in a fish and chip shop in Thornaby.
The young woman is said to have been racially abusive, shouting "Thornaby is for whites" at staff at Santonia Fish Shop, Laburnum Avenue, at around 8.40pm on March 6.
Police say a young man was also present and shouted abuse as well.
The woman is white, aged 17 to 18, around 5ft 2in, slim, pale, with dyed blonde hair in a pony-tail. She was wearing a dark grey bomber jacket, a white hooded top and white tracksuit bottoms.
The man was aged 18 to 20, slim, with short brown hair, and was wearing a black jacket, white shirt and black tracksuit bottoms.
Call Crimestoppers on 0800 555111 and quote reference: S1/34/2008.