Do private security personnel have the right to pursue their suspects onto private property without backup?

A national chain store in the neighborhood was supposedly chasing a thief on our street & says they came into our yard,which may or may not be true. I called the local Police because I thought that he was attempting to break into the yard. I only saw ONE male suspect. The Police arrived & there was no one else in the yard expect me. No signs of entry & no footprints or broken plants & I certainly did not let anyone in the house. He told the Police I did & now they seem to believe this creep who I caught trying to break-in. What can I do. I want this man prosecuted. California.

Yes they can, they go through licensing and have a some ability to do things like this. As a citizen making a citizen arrest you could too, if Simone is committing a crime you have the right to arrest.

Check your state's laws and regulations on private security.

Yes, private security personnel have a right to pursue a suspect onto private property, provided that they do not forcibly enter a fenced yard or private residence. Anything privately owned is considered private property, so even places like a shopping center parking lot is considered private property. A security officer does NOT have the right to enter your yard if it is fenced. He must contact the Police to pursue anyone into a locked, private dwelling. But, all of these rules are different if the security guard is actually an off-duty Police Officer. Keep in mind, (non-Police) security guards do not have powers of arrest or other legal powers that Police do. They can and should be arrested for breaking the law.