ROYAL OAK, Mich.—On a September day last year, a physician walked unaccompanied into Target Sports, a big gun shop and shooting range here, rented a gun, pointed it at himself and fatally pulled the trigger.

Then, four days before Christmas, another Target Sports customer, a 23-year-old Royal Oak woman, fired a single shot to her head while on the indoor gun range. She died later at a local hospital. One evening a month later, a third visitor fired a gun into his chin at the range and abruptly left the store before police...