They can search anywhere they have reason to believe the parolee has access to. If there is the remotest belief that the parolee has access to a room, that could justify a search of the room.
People who live with probationers/parolees cannot "reasonably expect privacy" in shared areas of the residence. (Pleasant (2004) 123 Cal.App.4th 194, 197.) Thus, an objection of the cotenant (roommate, spouse, etc.) cannot prevent you from conducting a search of the shared areas. However, you cannot search areas that are occupied or controlled exclusively by the cotenant. You must limit your search to those areas exclusively occupied by the probationer/parolee or those areas that are jointly occupied by the probationer/parolee and the cotenant.
As for a specific item, you need some basis for thinking it belongs to or is under the control of the probationer/parolee in order to search it. This basis may be supplied by the surrounding circumstances. (Britton (1984) 156 Cal.App.3d 689, 700-703; Baker (2008) 164 Cal.App.4th 1152, 1159.)
If they find contraband not belonging to the parolee, the person owning it or whose property was searched can seek to have it excluded at his or her trial.
The long and short of it is that if you choose to live with a parolee, you run the risk of being searched.