Rhondda Cynon Taf Council passed a motion on Wednesday calling for Cwm Taf to do everything it can to rebuild public confidence in health services.
It's calling for the chief executive - who is currently on sick leave - to consider her position.
It follows a series of "serious failings" at Cwm Taf Morgannwg Health Board.
In April, the health board's maternity service was placed into special measures following an investigation into the deaths and serious injuries of babies.
The no confidence vote came just hours after it was announced that the chief executive of the health board is on long term sick leave.
The Chair of Cwm Taf Morganwwg health board, Marcus Longley, said Allison Williams is on an "extended period of sickness absence".
The leader of Rhondda Cynon Taf Council, Andrew Morgan, said it was important to "reassure people that it is safe to use maternity and other medical services within this County Borough".
He added: "At present, I don't have confidence in the Health Board [...] simply because when I have regular briefings with them, I don't know if I can trust those briefings".