Garda Commissioner Drew Harris is to be asked to check with local garda stations for any cases of bullying as well as any evidence of fraudulent sick notes for members of the force.
The move by the Public Accounts Committee (PAC) also comes amid concern about gardaí filling in 'exit surveys' when they leave their jobs.
PAC chairman Sean Fleming outlined how Mr Harris had written to the committee with details about three cases involving the altering of medical certificates and claiming of allowances whilst on sick leave. One was found not to be in breach of discipline while the other investigations are still ongoing.
He was also asked about any bullying claims evident in exit surveys completed by departing members.
PAC members were not satisfied with his letter and want more information on both matters.
Sinn Fein's David Cullinane said bullying complaints may be logged at a local level. He also wants any details about suspected fraud, particularly involving sick notes. One case has gone to court.
Social Democrats TD Catherine Murphy criticised the use of exit surveys for supervising gardaí. “That is not the way to go if you want change,” she said. She also said it was not clear if allegations about fraud and any garda allowances were "small" or if they were more widespread.
Independent TD Catherine Connolly said the garda commissioner's answers on bullying and fraud were “not reassuring replies”.
Mr Cullinane asked whether garda chiefs had done a trawl of local garda stations to check for any bullying allegations.
Meanwhile, a whistleblower has alleged to the PAC chairman that resources for special needs supports in a school have been "misappropriated". Mr Fleming said the person who had come forward with the details claimed there had been a “misuse of public funds”.
The PAC will now seek a detailed response from the Department of Education on audits of schools and any details of misuse of funds.
However, Ms Murphy said she would not be surprised if such problems were not happening in other schools. She also wants education chiefs to explain what controls and inspections are in place to prevent such abuses of funds.