I have heard that it is against the law to leave a child alone in his
own home who is under 12 or to allow a child to babysit (watch other
children) who is under 13.  Is there any basis for this in fact?  The
location is the state of California, county of San Bernardino.

I searched Google under "child endangerment" + California + law, as
well as searching the California penal codes and could not find an
answer.

I would accept an answer that factually proves or disproves this assertion.

This is not a legal matter, just to resolve a family argument.

Thanks

Hello and thank you for your question

The answer is yes, there is some basis for this, but no, there is no
such specific legal requirement.

Under California Code Section 11165.2, "neglect" means the negligent
treatment or the maltreatment of a child by a person responsible for
the child's welfare under circumstances indicating harm or threatened
harm to the child's health or welfare.  The term includes both acts
and omissions on the part of the responsible person.
 ....
   (b) "General neglect" means the negligent failure of a person
having the care or custody of a child to provide adequate food,
clothing, shelter, medical  care, or supervision where no physical
injury to the child has occurred.
http://www.leginfo.ca.gov/cgi-bin/displaycode?section=pen&group=11001-12000&file=11164-11174.4

So although there is no specific rule about leaving a child home alone
or with an underage babysitter, it would be a question of fact whether
in a specific case that conduct consituted "general neglect" in the
form of a negligent failure to provide adequate supervision of the
child.

There is a specific form that one would use to report general neglect,
and in many cases there is a legal obligation to file the form if the
neglect exists.
Child Abuse Investigation Report
http://caag.state.ca.us/childabuse/pdf/caci_regs.pdf
(page 5)

See
Child Abuse Statutes and Regulations
http://caag.state.ca.us/childabuse/regulations.htm

Note that if a child is being neglected, the form is filed and an
investigation is warranted even if the child has not at that point
suffered any specific harm.

Search terms used
california child ~neglect ~statutes 

Thanks again for bringing us your question.  If you find any of my
answer unclear, please request clarification.  I would appreciate it
if you would hold off on rating my answer until I have a chance to
reply.

Sincerely,
Richard-ga