More than two dozen times during the past eight months, Duray A. Smith worked at least a partial day supervising state child abuse investigators — as well as a full day substitute teaching.

At least that’s what his time sheets say.

Smith, a child protection supervisor with the Department of Children & Families in Miami, billed the state agency on about 30 occasions since late October for at least a partial workday on the same day he is listed as a substitute teacher with the Miami-Dade School District, records show. The time sheets do not include the exact hours Smith worked, so it’s unclear if he double-billed the state and the county school board.

Though DCF requires its employees to obtain permission before taking on a second job, Smith’s personnel file shows no evidence he informed his bosses of his moonlighting.

Embroiled in one of the agency’s worst scandals in recent years, Smith abruptly resigned on Thursday. “Please accept my letter of resignation effective immediately,” he wrote in a terse email to DCF’s top Miami boss, Southern Region administrator Esther Jacobo.

Another supervisor, Tracey Wadsworth, was placed on administrative leave Thursday, Jacobo said. The investigator in the case, Shani Smith, no relation to Duray Smith, already is under suspension. DCF Secretary David Wilkins said both his agency’s inspector general and the Miami-Dade state attorney’s office are looking into whether Shani Smith concocted a substance abuse evaluation that was never performed.

The investigator and two supervisors are under intense scrutiny as DCF administrators try to figure out what went wrong in a case involving an 11-month-old Kendall boy who died May 16 when his mother left him strapped in a closed, hot car, along with her purse and a can of beer, and forgot about him. Child welfare investigators had evaluated his safety twice before his death, including after a November incident in which his mother, Catalina Marista Bruno, had been arrested for drunken driving with the infant unsecured in the front seat.

Jacobo declined to discuss Duray Smith’s second job on Thursday, saying the agency had been unaware of his moonlighting until she was questioned by The Miami Herald. “We have had no opportunity to review anything,” she said. Duray Smith could not be reached for comment.

At a time when agency heads insist they have “transformed” DCF to avert such tragedies, the death of Bryan Osceola has caused some children’s advocates to question the reforms’ success. The Community Based Care Alliance, which oversees Miami’s child welfare and foster care efforts, will discuss Bryan’s death at a meeting next week.

Bryan’s parents, Catalina Bruno and Amos Osceola, had been the subject of two calls to DCF’s abuse and neglect hotline during his short life. The first call was received on July 7, 2012, when Shani Smith wrote that Amos Osceola had been arrested for domestic violence after he “attacked” Bruno in front of her three children — Bryan, a 4-year-old and 10-year-old from a different father.

Four months later, Shani Smith investigated another report: Bryan had been found Nov. 3 lying on the front seat unsecured as his mom was “passed out” drunk in a Chevy Impala a few minutes before midnight near Krome Avenue. The hotline was told that Bruno was “driving recklessly” and had “hit several walls” before falling asleep in her car with the transmission still in drive. Though the Florida Highway Patrol charged Bruno with drunken driving and child neglect, Smith closed her investigation as unfounded.