Though additional research is still needed, based on a study published in Volume 22, Issue 2 of the Electroencephalography and Clinical Neurophysiology journal, their observed behavior suggests that frogs do not sleep in the same way that mammals do. Many species of frogs are only active at night, spending the daylight hours sitting motionless in safe, moist hiding spots, such as under logs. However, rather than normal sleep cycles, the frogs observed seem to stay in a state of alertness during these "rest" periods.
The only way to confirm if frogs are truly sleeping while they are sitting motionless during the day is to perform studies of brain activity. Sleep is very different from "turning off" and lying motionless. It is an active process characterized by cycles of special patterns of brain waves. There are four different stages of sleep, and sleepers also spend time in rapid eye movement periods during which dreaming occurs.
When frogs were observed, their brain activity suggested that they were not truly sleeping. When exposed to external stimuli, they were able to quickly respond to perceived threats, with none of the body response changes that typically mark a transition from "sleeping" to "waking" occurring. It is not a subject that has been extensively researched however, and additional studies are needed to get a more detailed understanding of a frog's actual sleep mechanisms, or if they truly exist.