Staff++supports Trello integration. Whenever reports are created, or they change status it can by synchronized with Trello. However this a one way synchronization, if you change the cards created by Staff++ in Trello it will not be updated in game.
Lastly map the Staff++ statuses to the correct Lists on your Trello board. The match is done based on the List name and it must be an exact match. If the plugin can't find any of the configured lists on the board, an error message will be thrown at startup of the plugin