Suffolk police are working closely with investigators in California to identify suspects who bilked residents here out of thousands of dollars.

Dozens of victims, many of them Suffolk residents, have lost more than $35,000 from their checking accounts after the thieves obtained their debit-card information. The victims, police say, all had one thing in common — they had purchased gasoline at Murphy USA on North Main Street, using their debit cards and personal identification numbers.

Within hours of the cards being swiped at Murphy’s pumps in Suffolk, unknown suspects in California had apparently manufactured copies of the cards and used them at automated teller machines in that state. The thieves first conducted a balance inquiry on each account and then withdrew as much money as they could.

Murphy USA representatives examined their equipment at the Suffolk station and said there was no evidence that the problem originated with them.

According to city spokeswoman Debbie George, a task force in California has obtained video from surveillance cameras near the ATM machines.

“They are working with California officials to try to get those subjects identified,” George said.

She added that fraud reports seem to have slowed.

“We have not had the constant influx we were having there for a while,” she said.