I don't think that's common, and I've never done it for people who've shadowed me, but my guess is they want to make sure there aren't any red flags before they expose you to their patients. I'd try someone from a former job or a professor.
It's up to the person who is going to let you in their clinic. They may just want to make sure you are not weird or have some bad character. You can get references from your professors, an employer, someone who works in rehab, maybe church. They can emphasize your qualities such as being punctual, devoted, expressed interest in PT (for references from pre-reques), hard-working, motivated, willing to help your classmates/co-workers when needed... things like that.
My last CI told me that he once had a student who was WILDLY inappropriate, he asked him to leave after one hour, and now has some sort of screening in place (I forget what exactly), so it may be that this PT is simply being cautious. In this spirit, I would submit references that can speak to your professionalism/conduct.
