The agency, the Florida Department of Children and Families, had been alerted to posts on Snapchat of Mr. Cruz cutting his arms and expressing interest in buying a gun, according to the report. But after visiting and questioning Mr. Cruz at his home, the department determined he was at low risk of harming himself or others.

The report is the latest indication that Mr. Cruz was repeatedly identified by local and federal agencies as a troubled young man with violent tendencies. The F.B.I. admitted on Friday that it had failed to investigate a tip called into a hotline last month by a person close to Mr. Cruz identifying him as a gun owner intent on killing people, possibly at a school. The local police were called to Mr. Cruz’s house many times for disturbances over several years.

Mr. Cruz also worried officials at his former school, Marjory Stoneman Douglas High in Parkland, Fla., who on at least one occasion alerted a mobile crisis unit to get him emergency counseling, according to the state report.