If I am backing out from a parking spot in a parking structure and I get hit from a driving car, who is at fault?

Typically, a vehicle backing out a parking spot is supposed to yield to the traffic traveling up and down the parking lanes, so this would make you at fault.  However, in most states, the police will not respond to accidents that occur on private property, like a parking structure, and thus most of the time citations are not issued.  This leaves it up to your respective auto insurance companies to determine who was at fault for the collision and the percentage of fault.  It is possible that both of you might be found to be at fault to some degree.