Our Lacey, will not even poop in the yard. She prefers to go to the wooded area in our backyard or a ditch in the front. When we were visiting relatives on a farm for a week she would walk out into the cornfield to poop. In fact she was visibly disturbed when the other dogs would poop in the yard. She would look at them as if she was thinking, "But why are you pooping in the playground?". Even if we picked it up she would avoid running over the spots while playing.

Lots more information needed here. As Debra asked, how old? How long have you had this dog? Is this a new behaviour and if so how recently has it appeared? What training have you done with this dog? IMO, it isn't unusual for a Basenji to object to doing something it doesn't want to do (or when asked to cease doing something it does want to do!), but usually this will be only a grumble and if it has escalated to biting or threatening to bite you need to deal with it, and if you aren't confident then you need help from a qualified trainer.