The Conservative group at Perth and Kinross Council has expressed outrage at the SNP choosing the convener of PKC's scrutiny committee.
The Conservative leader argued it should be for opposition groups to decide.
Meanwhile another Conservative councillor called it a "vile desecration of our local democracy".
The allocation of appointments to committees was put before councillors as they met on May 25 for the first time since the May 5 elections.
The SNP administration’s motion proposed - former Conservative now Independent - councillor Colin Stewart convene the scrutiny committee.
The Independents have not formed a coalition with the SNP. But prior to Wednesday's meeting all four Independents said they would support the 16 SNP councillors forming a minority administration. Labour said they would abstain. This then left it arithmetically impossible for an alternative administration to be formed.
Scottish Conservative group leader John Duff welcomed the "collegiate approach" taken by the SNP in the allocation of councillors to committees but added: "There is an important point of principle at stake in relation to one of the appointments being proposed by the administration.
"It has been the good practice and established custom of this local authority that the opposition parties have been permitted the opportunity to appoint the conveners and vice-conveners of audit and scrutiny committees. This was a custom and practice which was afforded by my group to the opposition in the previous administration when [ SNP ] councillors Drysdale and McCole chaired these two committees."
He said it was "good practice" and "provides transparency and credibility to the work of audit and scrutiny". The Highland Perthshire councillor told the chamber it "upholds the integrity and the public perception of the important scrutiny function".
He added: "I believe that it is vital the opposition parties are seen to appoint these roles without any perception that the administration has had a say in the decision."
Councillors were then asked to vote on whether the opposition should determine the conveners and vice-conveners of both the audit and risk committee and the scrutiny and performance committee.
All 16 SNP councillors and four Independents voted for the proposals put forward by the SNP. The 14 Conservatives and one Liberal Democrat councillor - Willie Robertson - voted for the conveners and vice-conveners of the audit and scrutiny committees to be decided by the opposition groups. The other three Liberal Democrat councillors and both Labour councillors abstained.
Speaking after the meeting Cllr Duff called the decision "shameful" and "disgraceful".
He said: "Today’s, quite frankly, shameful decision by the SNP to deny the opposition the right to choose the convener of scrutiny and to vote their own supporter into the post is disgraceful. This denial will have caused damage to the integrity of the committee’s work in the eyes of the public and have undermined the scrutiny process within the council. Nor does it support Cllr Laing’s call for a more collegiate approach to the way in which Perth and Kinross Council operates under an SNP minority administration.
"I believe that it is a fundamental point of principle that opposition groups appoint to these positions without any perception that the administration takes a hand in that decision. The new SNP administration shredded that principle today."
Newly elected Strathearn Conservative councillor Noah Khogali Tweeted: "This is a vile desecration of our local democracy and an overt attempt to evade scrutiny."
