Lopey said the woman had met the boys through a 'chance encounter' and developed a relationship with the boys at a later time, the New York Post reported.
The exact ages of the three students have not yet been disclosed.
According to her Facebook page, Fletcher has at least one daughter.
The dental assistant took down her Facebook account midday Thursday, after the allegations went public.
District Attorney Kirk Andrus told the news station that police could have arrested her at any time had they enough probable cause. However, the police did not arrest her sooner because she was not thought to be an 'immediate danger' to the community.
Andrus also said the case is sensitive due to the age differences between the parties.
"I have spoken with some of the victims... and you know, these cases are always challenging,' he said.
"I mean especially for a young person that are by definition not prepared for this kind of relationship.
"Relationship is probably the wrong word but they're not prepared for this kind of interaction with an adult."
No Mount Shasta High School teachers or employees were involved in the allegations.
Fletcher was jailed and later released on $10,000 bail.
She is scheduled to appear in court on March 22.