Cops are investigating whether at least seven tourists who mysteriously died in the Dominican Republic were poisoned by counterfeit booze, The Post has learned. Officials want to know who supplied the alcoholic beverages the victims drank in the minutes and hours before their deaths over the past year — and if the drinks had any dangerous chemicals in them, law enforcement sources said. The FBI is assisting and will take blood samples from the dead back to its research center in Quantico, Va., a source said.