Strictly speaking, Ohio law only requires a property owner to clear snow on public sidewalks (e.g., that border a public road) and the area around a fire hydrant. There is no provision in the Revised Code that deals with an apartment complex owner and a parking lot. However, if a complex owner neglects the property completely, he or she may be allowing a hazardous condition to exist. Arguably, someone might assert that the unplowed snow is a nuisance.
Given that you don't appear to live in the complex, you'll likely be ignored if you simply contact the owner. Your best bet is probably to talk with a resident of the complex and see if he or she is willing to contact the owner and highlight the danger / liability that the owner is creating.