The Convention of Scottish Local Authorities also warned that government promises to consult on proposed compensation payments were in danger of being exposed as a sham.
Local government minister Allan Stewart had originally said that members of the commission's predecessor body, the staff advisory committee, would be announced before 1 April.
Pat Watters, convenor of Cosla's personnel services committee, wrote to Mr Stewart this week pointing out that no names other than the chairman Robert Peggie had yet been released.
It was also difficult to see how Mr Stewart could uphold his promise to consult the advisory committee on compensation arrangements and 'avoid a situation where any consultative exercise is a sham because decisions have been taken in respect of England'.
Cosla asked Mr Stewart to confirm decisions on compensation payments in England and Wales would be delayed until the Scottish staff advisory committee had the opportunity to express its views.