When 6-year-old Julia Padrino showed up at Seminole Elementary with a visible wound on her left arm — explaining that her stepfather “bit me with his teeth” — police and child welfare administrators immediately investigated.

“It hurt,” she said.

Two months later, authorities concluded they had “no safety concern” about Julia and her younger siblings: By then, their stepfather had been sent to jail on an unrelated probation violation, taking him out of the house and putting the kids out of harm’s way. Julia’s mother promised to divorce him, and keep him away forever.

“The children are safe,” a Department of Children & Families report concluded.

Indeed they were — until six months later when Alberto Sierra was released from the Miami-Dade jail. Julia’s mom, who never followed through on the divorce vow, welcomed him back into her Flagami home.

The results were disastrous: Last week, 29-year-old Gladys Machado and her two young daughters were found suffocated and stuffed in the closet of an abandoned home. On Tuesday, Sierra told Miami-Dade police he killed Julia, now 8, her sister Daniela, age 4, and their mother in a fit of rage after Machado, in his presence, took a phone call from another man.

After killing them, he sexually assaulted the corpses of Machado and Julia, police say. He has been charged with three counts of first-degree murder and two counts of sexual battery.

Child welfare administrators said Wednesday they firmly believed Machado’s children were not at risk when they walked away from the family at the end of last year, and, in any case, did not believe they had authority to take additional action.

“At the time of the investigation, Ms. Machado took aggressive and decisive action — both by cooperating with law enforcement to jail the abuser and by voluntarily moving the children to their biological father — to keep them away from their abuser,” said Esther Jacobo, DCF’s top Miami administrator.

However, state child welfare and police reports, obtained this week by The Miami Herald, show authorities had several opportunities to intervene on behalf of the children, but chose not to:

•  Although a team of medical professionals concluded Julia had been the victim of “child physical abuse” — this only a year after he had allegedly bitten his wife during a fight — Miami-Dade police ruled that he had bitten the girl only “playfully.” The department chose not to arrest him.

•  Though a child welfare supervisor recommended that DCF refer Machado for social services to promote the safety of her children, the idea was dropped six weeks later. “Children appeared happy and there is no safety concern for the children at this time,” a report concluded.

•  Though DCF supervisor Osa Ogiemwanye, a veteran child protection worker, instructed an investigator to make sure the kids’ birth father petition a family court judge to grant him sole custody, the effort went nowhere. Michael Padrino did as he’d been urged, filing a handwritten request with the court. But when Padrino appeared at a hearing three weeks later, he was told his request was “moot” — because DCF had already given the children back to their mother.