A bracket doesn't bond as firmly to a permanent crown as it does to the surface of a natural tooth. When teeth with crowns are moved, the position of the edge of the crown relative to the gum can change, which means the crown has to be replaced after treatment. The contacts between the crown and the neighbouring teeth can also change and may no longer be tight, because the shape of the crown was designed for the position of the tooth before treatment. In general, a bracket bonds better to a temporary crown, and permanent crowns usually have to be replaced after orthodontic treatment anyway, so it's advisable to replace them with temporary ones before treatment starts.
This answer is for general information. Your own case needs an examination by an orthodontist.