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Police Chief Mike Peterson in the small, southeastern town of Preston said Friday the threats were vague but connected to the allegation that the puppy was fed to the turtle March 8 at the junior high school in front of students.
Officers were posted outside the town's schools this week.
There was no school Friday but Peterson said officers may return Monday.
Two parents have said the teacher fed the turtle a sick puppy. The teacher has not been named.
A prosecutor is investigating and Idaho officials seized the turtle Thursday, saying it's an exotic species requiring a permit.