The State Services Commission (SSC) sets standards of integrity and conduct applicable to most State Services agencies.
"What we saw last week, with holding a press conference for a senior public servant about whom serious allegations have been made, and against whom a finding of serious misconduct had been made...the idea of calling a press conference so he can give his version of events, that sounds to me more like a State Services Commissioner, in the form of Ian Rennie, taking leave of his senses and being unfit for the job," Mr Little said.
He told Q&A this morning the methods used to announce Mr Sutton's resignation potentially "alienating" sexual harassment complainants in the wider public service.
Mr Little said public servants who made complaints against their bosses had a right to know there would be "integrity" to the process.
"I think now we're entitled to conclude that Ian Rennie is unfit for the job and there has got to be now an investigation into his fitness to hold that job."
Last week Mr Rennie said the SSC had received only one complaint about Sutton's conduct and "acted on it immediately".
The Herald on Sunday today reported at least six women made "informal approaches about sexual harassment" before the complaint that led to Mr Sutton's resignation.
At Mr Sutton's tearful press conference on Monday, he offered an apology to the complainant. He added: "I may also have offended other women through my actions and I'm very sorry to them as well."
Meanwhile, other sources told NZME News Service there were problems with measures the commission put in place to keep Mr Sutton and the complainant at a distance while the allegations were being investigated.