Overall, homebirth is safe. In some regards it is actually safer than a hospital birth. However, in asking if it is safe, there is a hidden assumption that non-homebirths are the safety standard. It is interesting to note that no study has ever shown hospital births to be safer than homebirth. Here are some studies you can look up for more information.
The Cochrane Collaboration is the ultimate in evidence based research. This review of the research found no strong evidence of either homebirth or hospital birth being safer than the other. You can see all their recommendations for pregnancy and childbirth here.
The Midwives Alliance of North America maintains an extensive list of research about homebirth. You may be able to access some of the journals listed through your local library, or by getting a library card at a nearby university library.
Citizens for Midwifery maintains a list of resources regarding midwifery issues. Scrolling through this list will reveal several homebirth safety studies and fact sheets for you to use while educating yourself or others.
The Homebirth Reference Site maintains an index of homebirth research you can review. You can view the references, or click on them to see the research.
These lists of research ought to give you all the evidence you need for determining the safety of homebirth in general. Your birth attendant can help you determine if there are any unique circumstances that might make homebirth unsafe for your family.