Layton police shared part of the video on the department's Facebook page.
The man is seen walking around the master bedroom and standing next to the bed and crib where the woman and her child were sleeping.
The woman's husband said the family woke up to find the sliding glass door to their bedroom slightly open, KSTU reports.
The husband told KSTU he installed the nanny cam about a month ago to help watch over the couple's 2-year-old girl and 8-month-old boy.
Despite several electronics in plain sight around the bedroom, the husband said nothing was taken.
According to KSTU, the woman and child were not touched, but the man was caught on camera exposing himself with an iPhone in his hand.
Anyone with information is asked to call the Layton Police Department.
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