Conwy Council has passed a motion of no confidence against Betsi Cadwaladr University Health Board.
The motion, tabled by three councillors, called for the Health Minister to take control of the health board and for the Community Council to refer their decisions to the Minister.
It follows controversial changes to services in North Wales, which have sparked a series of public protests.
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Her suspension comes after she criticised Mr Hamilton for not supporting a policy on dignity and respect.