I'm sorry to see some mis-information posted here. CPM's are alive and well. doing homebirths in OH, as well as many other DEM's. They are easy to find online thru the Center for Humane Options in the Childbirth Experience (CHOICE) Ohio Midwives Alliance (OMA), Midwives Alliance of North America (MANA), North American Registry of Midwives (NARM, who oversees CPM certifications), Christian Midwives International (CMI) or the National Association of Parents & professionals for Safe Alternatives in Childbirth (NAPSAC) or just by asking around at libraries, health food stores, LLL meetings, etc.
The 2 midwives arrested were not "for nothing more than attending a birth" as stated earlier, but for practicing nurse-midwifery without a license (which could possibly have been argued against, but she pled guilty to that charge as a plea bargin for the worse charge of practicing medicine without a license) in one case, and for possesion & use of restricted items (ie. pitocin) and non-compliance with her parole officer (not revealing where she got the pitocin) in the other. No where in OH law does it say you need a license to practice midwifery. It only regulates CNM's (Certified Nurse Midwives)
CPM certification, though not eligible for licensure at present, is indeed "recognized" by the health dept. and by many doctors, cnms, & doulas. I can not only sign birth certificates as the "attendant" (but then so can the dad or anyone else who happens to be there) but CPM's can also sign the "proof of pregnacy" & "live birth" forms needed for filing the birth certificate, which may only be signed by a licensed medical practioner or a CPM, or a CPM in training.
So, back to your original question, no it is not illegal to have a homebirth with whomever you choose. And yes, you can sign yourself and your baby out AMA (against medical advise) although, if you do that the doctor has the right to refuse you further care, since you are "non-compliant" with his or her "orders".