Some communities have passed daytime curfew laws, probably to combat truancy or gang activity. These laws allow children to be cited if they are in any public place other than a school during the hours that schools normally are in session. Unfortunately, they are all written differently, so you need to read yours. But most have language something like this:
"It is unlawful for any minor under the age of eighteen years, who is subject to compulsory education or to compulsory continuation education, to loiter, idle, wander, stroll or play in or upon public street, highway, road, alley, park, playground, parking area, or other public ground, public place or public building, place of amusement or eating place, vacant lot, or any place open to the public in the unincorporated area of the County of San Bernardino, State of California, during those hours that his or her school is in session."
Notice the words "during those hours that his or her school is in session." This raises the interesting question of when schools where children are being taught at home are (or are not) in session. But you should assume, if you live in a community with a daytime curfew law, that police officers will think that any child out and about when the local public schools are in session is guilty of violating the law, even if you've given your child permission to go out for a while.
If you live in a community with a daytime curfew, HSC makes several recommendations for times when your child might be out in the community (such as at a park, library or restaurant) without you present. First, tell your child that if s/he is stopped without you there by a police or truancy officer, the child should not say that s/he is homeschooled. Tell your child to say that s/he is in a [charter school, public school independent study program, private school], whatever is the case. These officers don't like the "homeschool" word and it would be best not to trigger whatever negative associations they have with it. Second, you should make sure that your child has two things in his or her pockets. The first is a school identification card, which you can create on your computer at home (best if it has a picture of your child), giving the name/address/phone number of the school, child's name, age and grade (just put down what grade they'd be in if they were in school with their age group). You can laminate it (Kinkos can do that). The other thing to have in his or her pocket is a permission slip saying that the child has permission from the school to be off the property. Print up some slips with your school's name, street address and phone number at the top and with blanks for the date and time and name saying something like "On [write in the date], [print the name of school] ended its day at [write in the time]. The following student, [write in the name of student], has permission to be off of school property." Then have a signature line with a place for the signer to write his or her title under the signature.
Make sure your child is aware of the risk that he or she may be stopped and questioned by the police, tell him or her that he or she should be prepared to show the authority the school identification card and permission slip, and if possible give him or her a cell phone so s/he is able to get in touch with you at all times.
Also see: List of Communities With Curfews