They say 31-year-old Epitacio Cortina Jr. and 32-year-old Crystal Nichole Roberto are accused of shoplifting several power tools from a Home Depot store in Scottsdale last month.
Police say they received numerous tips that led investigators to identify Cortina and Roberto as suspects in the case.
They say the couple was confronted by store employees in the Oct. 13 shoplifting incident.
The employees told police the male suspect displayed a handgun and fled the store with the female suspect and the stolen items.
Police say the two drove off in a car that was later recovered and determined to have been stolen prior to the store robbery.