Home can be a wonderful place to have a baby, but it is the midwife who makes it safe.
I am involved in research involving midwifery education and standards around the world. The UNFPA report (State of the World Midwifery) is excellent for understanding how our standards in the US differ from the rest of the world.
CNMs in the US have education and training that is on par and equivalent to midwives throughout Europe. Almost every European country requires that the midwife first be a nurse and then complete a university based midwifery program. There are some small variations, but that is the standard. There are countries in Europe where midwives handle the majority of births in that country but those births also take place in hospital. So to expect that all midwives are doing home birth and getting excellent results is not true. In most European countries the home birth rate is less than 2 %, except for the Netherlands. However, in the Netherlands women are able to choose home birth only if they live within 15 minutes of the hospital, and midwives are limited in the number of birthing women they have in their caseload. In all European countries the midwives are licensed and regulated. They may only take care of women who have no risk factors such as elevated blood pressure, twins, breeches, diabetes, etc. Any woman who develops complications such as prolonged rupture of membranes, prolonged labor, bleeding, etc. must be immediately transferred to hospital. The midwife may continue care there, she may consult with the physician, or she may transfer care to the physician. If she fails to provide competent care in this way there will be an investigation and she may be censured. Midwives in Europe are much more integrated into the medical system. Most midwives are also required to carry liability insurance. All of the reasons listed above are why midwives in Europe can say that home birth is safe and why they have the statistics to back that up.
CPMs in the US must have a minimum of a high school education. Not a university education like most midwives in the rest of the world. They may or may not have attended an accredited midwifery program. And may or may not be licensed in their state. The laws regulating midwives in your state may be quite stringent or lax. They vary by state. The board that regulates midwives in your state may or may not make disciplinary actions public. If they don't then you have no way of knowing whether there have been complaints against that midwife and if she has been asked to take corrective actions. In some states the citizens maintain a database of complaints and discipline (Oregon) so the public is a bit more informed. Some CPMs may have a good relationship with a physician and will refer for an opinion or additional care and testing when risk factors appear. Others consider those risk factors a "variation of normal" and will not consult. This can be dangerous. Remember that in countries where midwives are educated, licensed and regulated , risk factors or complications require consult, referral, and transfer to the hospital. In the US with CPMs and especially with non-certified midwives there is no system in place to be sure the mother is transferred to a more appropriate level of care and usually there are no repercussions when the mother or baby are harmed or die. Most non-nurse midwives do not carry liability insurance. This means that if the parents want to sue to recover damages or to pay for ongoing medical care for the baby who has permanent damage, that the parents won't have a way to make the midwife accountable for her actions.
Non-certified midwives(DEM, community midwife, practical midwife, etc.) have no minimum educational requirement, not even a high school diploma. They are not required to study the basic sciences like anatomy and physiology and usually learn their trade through apprenticeship models. If the midwife they learn with doesn't know and understand these things, they may not either. They usually have little to no access to medications for postpartum hemorrhage and if they are illegal in your state they will not want to transfer you to the hospital when it is necessary or lifesaving, and if they do, they may not accompany you which means the hospital staff has no idea what has happened to that point, and it causes serious delays and disruptions in the care your receive. This makes the situation more life threatening.
One of the UNFPA's reports about midwifery says "Giving Birth Should Not be a Matter of Life or Death." Without knowing the qualifications, education, and competency of the midwife you may choose, home birth in the US may not be as safe as we would like to think.