A total of 32 students' details were released to Police Scotland during three years, from April 2011 to 2014, according to a Freedom of Information request.
The university said it passed information to police only "in exceptional circumstances."
They said they disclosed details if they were convinced failure to do so would prejudice a police investigation and that each disclosure was at the university's discretion.
Of the 32 students, nine were being investigated in connection with fraud, one for a bomb hoax, one for an historic sex crime, one for stalking, two for money laundering or drug trafficking, one for an illegal internet offence and two for theft.
Three others were investigated in connection with a missing person and six as possible witnesses in other cases.
The suspected crimes of the six remaining students were not specified. One of the 32 was a crime victim. The FoI request confirmed Police Scotland did not have to apply for a court order to obtain any of the disclosures.
A spokesman for the university said it adhered to "strict criteria" before passing on any personal information.
He said the safety and security of the students was "paramount".
He said: "We work very closely with the police and adhere to strict criteria before divulging any information about individuals.
"We consider each case very carefully and only act in exceptional circumstances - over the past three years this has involved 32 students out of a total student population of more than 23,000."
He stressed the numbers were low and the issues "potentially serious."
Gordon Maloney, president of NUS Scotland, said: "It is not and never should be the role of universities to be the eyes of the police on campus and we would be incredibly concerned if institutions were passing on information about students behind closed doors, without very good reason.
"We need protections to make sure information is not being shared inappropriately and students should be told that a request has been made, whether at the time or after the event."
Breffni O'Connor, president of the university's student council, said she believed the system on information sharing was "pretty robust".
She said: "We would be concerned if these requests weren't being treated very seriously. However we have no reason to believe they are not given proper consideration.
"We trust the university in that sense."
A Police Scotland spokeswoman said officers may be required to 'seek out personal information' during the course of an investigation.
She said: "Officers will therefore make enquiries with organisations who may hold this.
"The organisation will require to confirm that disclosure is appropriate in terms of the Data Protection Act; in relation to the prevention or detection of crime, or the apprehansion or prosecution of offenders."
Police must make all requests in writing, signed by Inspectors or higher rank.