Officers said they had now closed the investigation into the death of the maths undergraduate, David O’Halloran.
David, 18, disappeared following a night out with friends in January and his body was found three months later.
Earlier this week, David’s mother, Donna, 41, called for a fresh police investigation after an independent toxicology report found levels of club drug, GHB in David’s system.
The report was commissioned by the family and carried out by Glasgow University with tests on the urine and hair of the mathematics student revealing levels of GHB similar to those detected in fatalities involving the drug.
A spokeswoman for police confirmed they also had a toxicology report carried out and its results were made available to the family.
She added: “Our inquiries into the circumstances surrounding the death of David O’Halloran have concluded.
“We have worked with David’s family and kept them informed of our investigations. We are aware of the suggestion David’s drink may have been spiked but our investigations have shown that there is no evidence to prove this.”
Asked if, in the light of the independent toxicology report’s findings, they intended to reopen the case, the spokeswoman added: “Investigations into the circumstances surrounding David’s death have been extensive.
“They have been carried out over a long period of time and the inquiry into his death has now concluded.”
Mrs O’Halloran said she had always been of the view that her son’s drink had been spiked and said: “He was not a drug user.
“I firmly believe his drink was spiked and if that is the case then someone out there is guilty of manslaughter.
“The police have to look at this again or we should have a fatal accident inquiry.”
GHB (Gamma hydroxybutyrate), is an anaesthetic with primarily sedating rather than painkilling properties.
It is often sold as ‘liquid ecstasy’ because of its relaxant and euphoric effects, although it has no relation to ecstasy.
It was made illegal under the Misuse of Drugs Act in 2003.
Tests on David’s body found he‘d had apparently high levels of GHB in his system for four months.
It is understood that police have been advised that because the substance is naturally occurring in the body’s central nervous system it’s not clear what is a ‘normal’ level.
Tests could not indicate whether David had taken the drug himself.
Mrs O’Halloran said she was “disgusted” by the decision to close the file on her son’s death, insisting all the evidence pointed to his drink being spiked, and now intends to push for a fatal accident inquiry.
She said her son’s death certificate concluded his death was “unascertained” and added: “If he had a drug habit I would have found evidence in his bedroom, or either I or the police would have found something in his room at university because, like all teenagers, he was not exactly tidy.
“His friends said there’s no way David would take anything like that. He didn’t smoke. He loved his body and was a sociable drinker.”
David, from Kilmaurs, Ayrshire, went missing during the early hours of January 18 after a night out with pals in Stirling.
He was wearing only a t-shirt, jeans and a shirt on a night when temperatures plunged to minus four.
He was dropped off by a taxi about a mile from the campus but was last seen at about 2.20am in Bridge of Allan walking away from his accommodation.
His body was found on April 16 on farmland above Bridge of Allan following an extensive search.