I had exactly that relationship when I started 22+ years ago. I started with a chiropractor first and then expanded out...
I had a background in the medical field first and so I had lots of connections.
They won't even entertain the idea of working along with you unless you present professionally, have a knowledge and background of how medicine can integrate with massage, be able to explain how their modalities and yours complement each other. Know your anatomy well, medical terminology and pathology.
Once you feel well prepared and educated, offer them a free session too. Have professional brochures or information that shows "proof" how certain massage techniques have helped "specific" modalities.
I even set up an adjunct massage program within a PHysical therapy program at a hospital on Hawaii. So I KNOW it's all possible.
Doctors especially are busy and don't have the time, their office manager or receptionist might be the one you have to convince first ;) (hint). I was an office manager for a neurologist years ago.
Chiropractors are generally easier and more open to working along with MT's.
Orthopedists were also advocates of mine.
In my experience, the chirporactors are the most accepting of what we do and around here (Michigan) most of them have or refer to a massage therapist...so it's a good point of entry. A couple of the hospital systems have massage therapists, especially in their oncology departments (which is where the alternative/complimentary can usually be found) but hospitals are hard to get in with around here because there isn't much employee turnover.