Here is a link to the ACLU's "Know Your Rights - Free Speech, Protests, and Demonstrations in California:"
http://www.aclus.org/our-work/know-your-rights/know-your-rights-free-speech-protests-and-demonstrations-california
There is more for you to consider, dannydanush, than simply whether you are on a public sidewalk or not when distributing your leaflets. Although trespassing is something you need to avoid (which means you will need to know what is public and what is private property), you will also need to know if a permit is required under your local ordinances (it probably will be) before you can distribute your leaflets. There will be reasonable "time, place and manner" restrictions, so you do not disrupt the public or disturb those who work in the doctor's office.
Your concern, seeing as how you placed this in the defamation section, appears to be what you can and cannot say about the doctor. Anything you write in your leaflets or that you say to passers-by should be provably true or pure opinion (opinion that does not state or imply any false facts). If you are able to state ONLY the facts of the experience your wife and child had during childbirth, without exaggerating these facts or embellishing these facts or inventing facts or implying false facts or generalizing or drawing conclusions about the doctor from your single personal experience, you might avoid defaming the doctor - but you will not necessarily avoid legal action being taken against you.
You have to remember that you will be handling a professional's reputation, and these reputations are valuable. Harming the doctor's reputation can be costly.
I am sorry your wife and your child had a difficult time. It is best for you to review the facts of your child's birth with a malpractice attorney before making negative public statements about the doctor. You should be able to find an attorney in your area willing to go over the facts of the birth and to also go over with you all of the risks you face in distributing leaflets that make derogatory comments about a professional person, especially when this professional person has not been sued for malpractice and has not been charged with any crime.
The ACLU link provides an outline of your rights and your risks. The attorney you see can help fill in this outline.