Interviewing for Lab Department Head

This isn't exclusively POC, but I figured this resourceful group would have some input.  My facility is in the process of interviewing for a new laboratory department head and has put together a peer interview team.  I don't have a lot of experience with HR or interviewing, so I'm looking for suggestions for possible questions to ask the candidates.  We will be "coached" prior to the actual interviews but were encouraged to bring our own potential questions.  Thanks for your help!