WXYZ-TV reported that Farmington Hills police had responded Sunday morning to a report of an assault at the Green Hills Apartments, northwest of Detroit.
Officers heard shots inside the apartment after announcing their presence.
Other residents in the apartment building were evacuated. A county Special Response Team later found the man and child dead inside the apartment. A shotgun was found next to the man. It was not immediately clear how the child died.
Police said the shooting may have stemmed from ongoing divorce proceedings.