We don't have to approve who he chooses, though most of the time we do. I'll try to work cooperatively and effectively with most anyone, so I've rarely had objections to his appointments. After all, presently, they're his to make, and, usually, a fellow resident. The majority of trustees usually goes with the mayor's appointment.
There has only been one attempted appointment that was rejected by the board, since I've been elected. I believe it was a poor choice, initially, and a good decision was made by the board of trustees to stop it. A much better choice was presented the second time around, and approved.