Good question, however, a bit more background would be helpful. There have been users in the past who have asked similar questions with topics deteriorating into train wrecks of their personal problems. Maybe provide a bit more clarity on your background and rationale for posting and I'm sure you'll get some informative replies
I have never worked anywhere(I'm in south Texas) that you could absolutely refuse to transport anyone. We could suggest they wait and see there PCP, or drive themselves to the ER; but ultimately if the patient wanted to be transported we had to do that.