Puckett was charged with the theft of cash from a woman making a night deposit at the National City Bank branch in Troy a week ago. He is being held in the Miami County Jail.
Police said a stolen vehicle, used in several of the robberies, has been recovered.
Puckett appeared in a Miami County courtroom on Thursday morning, where bond was set at $20,000.
Officers said they believe at least one or two other people were involved in committing the crimes.