In another tweet, which also appears to have been deleted, Rice urged Southwest to rewrite its safety policy, according to the Arizona Republic.
Responding to Rice's tweet, Southwest said: "We appreciate your concern and sharing this information with us, Todd. We assure you that Safety is our top priority and are addressing the situation."
Southwest allows trained emotional-support animals to travel on domestic and international flights as long as their handlers provide health certificates, permits and vaccinations required by the "country, state or territory from and/or to which the animal is being transported."
The incident comes as two major airlines have changed their policies in response to an uptick in the number of reports involving animals on commercial flights.
Delta Air Lines said in January that it is requiring advance documentation, such as proof of health or vaccinations and signed paperwork confirming that the animals can behave.
The new requirements are in response to an 84 percent increase in incidents since 2016, from urinating or defecating, to barking or growling, to mauling a passenger whose face needed 28 stitches. Delta said it carries nearly 250,000 service or support animals each year.
"The rise in serious incidents involving animals in flight leads us to believe that the lack of regulation in both health and training screening for these animals is creating unsafe conditions across U.S. air travel," John Laughter, Delta's senior vice president, said in a statement.
United Airlines announced similar changes earlier this month. The new policy also comes on the heels of dramatic increases in the number of passengers flying with comfort animals. About 76,000 flew last year, nearly double the 43,000 in 2016, United spokesman Charlie Hobart told USA Today.
Federal guidelines specify that airlines must allow passengers with disabilities to board with trained service or emotional-support animals of many stripes, regardless of the animal's potential to "offend or annoy" others on the plane, The Washington Post reported.
But airlines have latitude to deny boarding to certain "unusual" service animals, including snakes and other reptiles, ferrets, rodents and spiders, and can prevent them from boarding if the animal poses a threat to the safety of others.
A few weeks ago, United denied boarding to a peacock named Dexter because it did not meet the required weight and size.
Shortly before that incident, a student who was on a Spirit Airlines flight said she flushed her dwarf hamster named Pebbles down an airport toilet after an airline representative told her to do so.
A spokeswoman for the low-cost carrier confirmed that an employee had incorrectly told the passenger that she could bring her emotional-support animal on the flight but denied that an employee told her to flush the hamster, The Post reported.
