OKLAHOMA CITY — Jerry Starr thought he was taking the safe approach when a twister was reported heading toward his suburban neighborhood outside Oklahoma City last May. He grabbed his teenage daughter Dyonna and his dog and drove to the local City Hall, which serves as a public storm shelter.

But when he arrived, a police officer told him that the only way they could come in was if Tobi, his shih tzu-yorkie mix, stayed outside. No pets allowed. So Starr and Tobi rode out the storm in his car, one of the most dangerous places he could be.

“I love her and there’s no way I was going to live knowing I was abandoning her,” said Starr, of Del City.

Modern forecasting technology now gives residents hours of notice of threatening conditions and precise projections of a storm’s likely path. Residents are bombarded with broadcast warnings to take shelter.

But as the spring storm season arrives in Tornado Alley, emergency officials are still wrestling with a dilemma posed by man’s best friends. Since many public shelters won’t accept animals, people wind up dashing across town to rescue their pets or staying in unprotected houses rather than hunkering down in safety.

“Pets and sheltering is always a problem,” said David Grizzle, emergency management coordinator for the college town of Norman, which closed its public shelters last fall because of problems with pets and overcrowding.

“Pets come in and sometimes they’re hard to control,” he said, describing past scenes of dozens of frantic dogs along with snakes, chickens and even iguanas brought inside.

Access to shelters has gotten special attention in Oklahoma this year after 79 tornadoes strafed the state in 2013, the second highest total in the nation, killing 34 people and injuring hundreds. Most of the victims were in cars, houses or unreinforced buildings. A joint state-federal program offered up to a $2,000 rebate to help eligible homeowners install fortified “safe rooms” or above or underground shelters.