Hunmanby ward councillors Michelle Donohue-Moncrieff and Paul Riley have stepped away from the group, which was formed following this month's local elections.
It leaves the group with eight members and Cllr Donohue-Moncrieff told the Local Democracy Reporting Service that she and Cllr Riley felt "disrespected" not to have been fully consulted on a move to partner with the minority Labour leadership to run the council.
"There has not been clear communication on what the arrangement is between the Independents and Labour," she said.
"I was not consulted on the final terms and there has been no discussion about policy and what we are working towards. I need to know what I am signing up for."
The 13 councillor Labour Group needs the 10 Independent Group members and two Green Party councillors to have control of the 46 person council. Last week, it was announced that an independent group member, Cllr Janet Jefferson, would join Cllr Siddons' cabinet as part of the deal.
Cllr Donohue-Moncrieff says she is not ruling out rejoining the group if she gets some clarity on the situation or even setting up her own with Cllr Riley.
She added that the move was not part of any plan to undermine the new leadership.
She said: "This not part of any Machiavellian plan to remove the leader, Cllr Siddons has been elected by the council he deserves the time to put forward his and I will not support any moves against him or votes of no confidence."
Scarborough Council will meet again on Thursday (30th) to elect councillors onto its various committees.