oslc_cm:status and rtc_cm:state are read only and cannot be updated.
OSLC does not define a way for updating the state yet and hence it is not yet supported.

workaround: https://jazz.net/wiki/bin/view/Main/WorkItemAPIsForOSLCCM20 for rtc_cm:state states: The status of the work item (modifiable via action).
Value can be one of the user-configured values in the process configuration of the workitem's project area.
--> Use Firebug to infer what parameters to use with OSLC put in order to implement such action
example: action=com.ibm.team.workitem.taskWorkflow.action.startWorking&itemId=_IY_2MDoAEeKwGL6SXKN-Dw&type=task&stateId=_IZXpoToAEeKwGL6SXKN-Dw&additionalSaveParameters=com.ibm.team.workitem.common.internal.updateBacklinks&sanitizeHTML=true&projectAreaItemId=_FxnkQDoAEeKI-JCkPh__hw
which seems coherent with the answers Patrick provided in https://jazz.net/forum/questions/32674/change-workitem-state-via-rest