Reference checking should be performed by the same person who is doing the interviewing, or at least someone actively involved in the hiring process – or you could use an outside professional reference and background checking firm. (I know a great company with highly trained people who can handle reference checking extremely well!)
Far too often, however, the task of reference checking is delegated to a clerical person who hasn’t been trained to do it, and the result is that follow-up questions aren’t asked and many areas of concern aren’t covered or just glossed over lightly. If you are doing the interviewing, you know what the job requires, what the challenges the person who is hired must face, what the personalities on your team are, and so on. That makes you, if you’re the hiring manager, the person most likely to know what specific follow-up questions to ask references. If the HR Department is small, outsourcing the time-consuming exercise of doing thorough reference checking to a firm with many years of experience doing reference checking might be an attractive alternative. A really capable firm will have people who will ask you what the job requires and what challenges the person who is hired will face and will always ask you if there are any additional areas of concern that should be covered when talking to references – that way the reference report will be tailored precisely to fit the requirements of the job.
The point is, regardless of who does the reference checking, it needs to be somebody who really knows how to do it. Reference checking should never be looked upon as an afterthought, but as a critically important part of the hiring process.