Entertainment Tonight reported on its Web site that Blosil jumped to his death Friday night from a downtown Los Angeles apartment building.
Officers responded to an apparent suicide jump in the area, but the victim was not identified Saturday, Los Angeles Police Officer Gregory Baek said.
"My family and I are devastated and in deep shock by the tragic loss of our dear Michael and ask that everyone respect our privacy during this difficult time," Osmond said in the statement.
Blosil reportedly left a note which referred to a lifelong battle with depression.
In 2007, Osmond said Michael was treated at a rehabilitation facility, but she didn't disclose the nature of his problem.
Donny Osmond, Blosil's uncle, told Entertainment Tonight: "Please pray for my sister and her family."
Michael is one of Osmond's five adopted children. She also has three other children from two marriages. She divorced Brian Blosil in 2007 after two decades of marriage. She and her first husband Stephen Craig divorced in 1985.
Osmond earned fame at age 13 with the hit song "Paper Roses," and starred with her brother, Donny, on television's "Donny and Marie Show" during the 1970s.
They perform a musical variety show regularly at the Flamingo Las Vegas Hotel and Casino. The hotel said Saturday's performance was canceled.
