Does anyone know the process for Civil service?

This is the situation below:
If I signed the offer letter with Statboard A reluctantly, and 1 week later before starting work I receive another offer letter from another government agency (Statboard/Ministry) which is what i really want, is there any penalty for doing such a thing?

My concern is if I will be blacklisted in the gov system, and if the new government agency, during the offer stage, will be able to trace I signed something with Statboard A previously?