I don't know if this is a general rule, but I had an open work permit under the Youth Mobility Agreement between Sweden and Canada, and they only required a medical exam if you wanted to work in health care, teaching or some other profession I can't remember (I think it was child care). I applied without a medical and they just issued me a work permit that said it was not valid for those fields.
They did require criminal checks. That being said, this is a special program, so I'm not sure how this relates to "regular" work permits.