United Airlines, under siege over the death of a puppy on one of its flights, says the flight attendant who ordered a passenger to put her pet carrier in the overhead bin didn’t know there was a dog inside.

The airline’s account was contradicted by the family that owned the French bulldog, and also by other passengers on Monday night’s flight.

Eleven-year-old Sophia Ceballos told NBC News that her mother told the flight attendant “‘It’s a dog, it’s a dog,’ and (the flight attendant) said we have to put it up there,” in the bin.

Other passengers backed up the family’s account on Twitter and Facebook.

United acknowledged today that the customer said there was a dog in the carrier. “However, our flight attendant did not hear or understand her, and did not knowingly place the dog in the overhead bin,” the airline said in a statement. United declined to identify the employee.

Last year, 18 animals, mostly dogs, died while being transported on United — three-fourths of all animal deaths on U.S. carriers, according to the Department of Transportation. Those figures represent animals that die in cargo holds.

It is rare that an animal dies on a plane. Even on United there was only one death for roughly every 4,500 animals transported last year.

United, which promotes its pet-shipping program called PetSafe, carries more animals than any other airline, but its animal-death rate is also the highest in the industry. Alaska Airlines, which carries only 17 percent fewer animals, had just two deaths last year.

“The overwhelming majority (of deaths), according to medical experts, were due to a pre-existing medical condition or the animal wasn’t properly acclimated to its crate,” said United spokesman Charles Hobart.

Hobart said the airline investigates every injury or death to an animal in its care. Pets are loaded last and taken off the plane first after landing, he said.

United’s PetSafe has its skeptics.

“I think United tries to make a business out of pet transport with this program, but (airline) ramp workers are not veterinarians,” said Brian Kelly, CEO of The Points Guy, a travel website that first highlighted this week’s incident on a Houston-to-New York flight.

Reports filed with the government indicate that in most cases of animal death or injury last year, United took no corrective action. Some animals were deemed to have died of natural causes, others from cardiac problems or gastric dilation, a condition associated with eating too much. One dog died of heat stroke, and another animal escaped while being handed back to its owner and was hit by a vehicle.

United has suffered a string of incidents that generated bad publicity in the last year, including the violent removal of a passenger from a United Express plane to make room for a crew member, and the death of a giant rabbit — its Iowa owners sued the airline, which they said cremated the animal to destroy evidence about the cause of death.

The issue of pets on planes has gotten attention recently after United and Delta Air Lines announced tightened restrictions on emotional-support animals, including requiring a health form filled out by a veterinarian.

If your pet must travel, experts have several recommendations:

— The cabin is safer than the cargo hold. Pets too large to fit in an under-seat carrier must go cargo unless it’s a service or emotional-support animal.

— Ask the airline or look up its rules about things such as carrier size, and don’t force your pet into a carrier that is too small.

— Take nonstop flights to avoid layovers, which increase the chances your pet could be mishandled or left longer in the cargo hold.

— Avoid extremely hot or cold weather and busy periods such as holidays.

— Make sure your pet’s tags and your contact information on its carrier or crate are up to date.

— Tape a bag with a day’s worth of food to the top of the crate — just in case.

— If your pet flies in cargo, use your own crate instead of renting one from the airline; it will help get them acclimated and minimize anxiety.