Este Hull, a 7th-grade student at Preston Junior High, told the station that Crosland usually fed mice or birds to his menagerie of animals, which also include snakes.
"I feel a little bit better that it was a puppy that was going to die, not just a healthy puppy," she said.
Parents Annette Salvesen and Julie Johnson told KSTU that Crosland is the best science teacher at the school.
"If it was a deformed puppy that was going to die anyway, Cros(land) is very much circle-of-life," Salveson added.
In a statement, the school district said it was investigating the allegation.
"On March 7, 2018, Preston School District was made aware of a regrettable circumstance involving some of the biological specimens at Preston Jr. High. The event … was not a part of any school-directed program. We emphasize that at no time was the safety of students or staff compromised."
According to the Idaho Statesman, Dave Fryar, the sheriff of Franklin County, of which Preston is the largest city and county seat, said he had forwarded a report on the investigation to the county prosecutor.
Meanwhile, the East Idaho News reported that the alleged incident occurred after regular school hours.
The newspaper said parents and students regard Crosland as a popular teacher who has snakes and other animals in tanks around his classroom. Three former students, who asked not to be named, said Crosland previously had fed guinea pigs to snakes and snapping turtles during classroom demonstrations.
"He is a cool teacher who really brought science to life," one of the former students told the paper. "I loved his class because he had turtles and snakes and other cool things."
The News said Crosland had not responded to attempts to obtain comments. The Statesman reported that Crosland is still teaching at the school and has not been suspended.