Sarah DiGiovanni ran through a mental list of reasons a Covington police officer might have told her not to drive away from the gas station where she had stopped to fill up after taking her sick toddler to the doctor.

Her brake tag was current; she was pretty sure she didn’t have a tail light out.

Even so, her face was tense with worry as more police arrived at the Market Max on La. 25 and Covington Police Chief Tim Lentz approached her car.

Then the smiling chief introduced himself and handed her a $100 bill.

After a stunned moment, DiGiovanni dissolved into tears. “I have six children; money is very tight,” she said. “I’m overwhelmed — I thought I was in trouble.”

Similar scenes played out all over Covington on Tuesday morning, fueled by a $2,500 donation from an anonymous donor known only as Secret Santa, the name that was stamped on the bills.

Lentz got the idea from the Kansas City, Missouri, Police Department, whose giveaway was generating traffic on social media.

The chief gathered his officers together at headquarters Tuesday morning to give them their orders. “It’s a gloomy day, but we’re going to make it bright for some people,” he said.

“Go make some people happy,” he added as he handed three $100 bills to each of the officers who took to the streets, reporters and photographers in tow.

School Resource Officer Darren Powell, who has two young children of his own, was on the lookout for someone with kids to give his allotment of the Secret Santa money.

He found one target in the toy aisle of Big Lots. Tonya Polk was shopping with her five children: Gabrielle, 11; LaQuintin, 9; Hayleigh, 6; Gregory, 4; and Sydiny, 3 months.

The surprised mother gave Powell a hug. As she loaded up the car with toys, she said she had let everyone pick something to take home.

Powell then headed to Rouses Supermarket, where he spotted another family with children. Katie Rivers didn’t realize she was being tailed as she chatted to her father on her cellphone. But her 9-year-old daughter, Angelina, noticed the uniformed officer and journalists, glancing back curiously as they tracked her family down the aisles.

Finally, Rivers realized she was being followed. She said she felt like crying, too. The money was definitely welcome this year, as her family has grown larger. Her grandchildren, 4-year-old Adrian Pittman and 1-year-old Karma Mathieu, moved in with them about three months ago.

“If I had known, I would have put on some makeup,” she told Powell. The officer assured her that he didn’t get any advance warning he was going to be photographed, either.

Lentz described the Police Department’s mission as building social capital, and the giveaway made an impression that went beyond those who got an unexpected $100.

Pat Patterson, who was shopping at Rouses, saw Powell give the money to Rivers and was clearly moved. “That was awesome,” he told the officer. “It shows that Christmas is still here.”

Customers who saw Lentz give DiGiovanni the $100 also called out their appreciation, saying they were glad to have witnessed the special moment.

“Giving is the spirit of Christmas,” DiGiovanni said. “I love this city, and I love St. Tammany. I feel blessed.”

Follow Sara Pagones on Twitter, @spagonesadvocat.