Laura Whitehurst, 28, pleaded guilty last week to having sex with her 17-year-old student.
There were questions about whether the school district violated the state's "mandated reporter law" because it did not notify police about an unsubstantiated rumor about the teacher prior to her arrest.
The District Attorney's Office on Friday announced an investigation determined the school district did not violate the law.
"Despite the hurtful rush to judgment in some quarters, it was always clear to me - and I think to anyone who had all the facts - that no violation on the part of RUSD administrators had occurred," said Superintendent Lori Rhodes said in a statement.
Whitehurst pleaded guilty to six counts of felony sex charges. Under the deal, Whitehurst will receive one year in jail and must register as a sex offender for life. She will also be under probation for five years, and she will have to forfeit her teaching credentials.
The judge ordered Whitehurst to stay away from the 17-year-old. The formal sentencing will be on Aug. 28.