Research

Numerous scientific studies show that homebirth with a midwife is as safe as (and some say safer than) hospital birth.

These studies include:
Largest Study on Waterbirth Finds No Harm To Babies. 2016.
MANA Statistics Project Analysis of Outcomes of Care for 16,000+ Planned Home Births in the US. 2014
Meta Analyses Comparing Planned Hospital Birth to Planned Out-Of-Hospital Birth. 2012.
Perinatal mortality and morbidity in a nationwide cohort of 529,688 low-risk planned home and hospital births ~ This study shows that planning a home birth does not increase the risks of perinatal mortality and severe perinatal morbidity among low-risk women, provided the maternity care system facilitates this choice through the availability of well-trained midwives and through a good transportation and referral system. BJOG, November 2009.
The Safety Of Planned Home Birth With Registered Midwife ~ The risk of infant death following planned home birth attended by a registered midwife does not differ from that of a planned hospital birth, found a study. CMAJ (Canadian Medical Association Journal), September 1, 2009. Found in Medical News Today.
Outcomes of planned home birth with registered midwife versus planned hospital birth with midwife or physician, Canadian Medical Association Journal, September 15, 2009
Outcomes of Planned Home Births with Certified Professional Midwives: Large Prospective Study in North America, British Medical Journal, 2005
The Decline in Maternal Mortality in Sweden: The Role of Community Midwifery, 2004
Outcomes, safety, and resource utilization in a collaborative care birth center program compared with traditional physician-based perinatal care, 2003
Midwifery care, social and medical risk factors, and birth outcomes in the USA, 1998
Meta-analysis of the safety of home birth, 1997
Outcomes of 11,788 planned home births attended by certified nurse-midwives. A retrospective descriptive study, 1995
The Safety of Home Birth: The Farm Study, American Journal of Public Health, 1992
Outcomes of care in birth centers. The National Birth Center Study, 1989
Neonatal Mortality in Missouri Home Births, American Journal of Public Health, 1987

One study is unsupportive. This study is flawed because it did not differentiate between planned homebirth and unplanned homebirth. Outcomes of Planned Home Births in Washington State: 1989–1996, 2002
Reading Scientific Birth Studies Critically: Washington State Home Birth Study