The laws vary from state to state. I'm not going to read them all. Here are the laws in my state:
http://www.kansas.gov/ksbtp/statutes.html
Specifically pertaining specifically to who does or doesn't need a license:
http://www.kansas.gov/ksbtp/74-7035.pdf
I've always thought a phlebotomist is similar to a licensed electrician. (Assuming an MD is similar to a PE)