In CA, the elements of a defamation claim are: 1) intentional publication of a statement of fact 2) that is false 3) unprivileged 4) has a natural tendency to injure or which causes "special damage," and 5) the defendant's fault in publishing the statement amounted to at least negligence.
The press does have a lot of rights, including the right (even the duty) to print legitimate news to inform the public. Truth is an absolute defense to a claim of defamation, and your arrest did happen, and you did take a mug shot. You can't shoot the messenger - it's your arrest that's damaged your reputation, not the press publicizing it. You won't have any luck getting the press to take the article down.
As for the police statements, if the were false, and not just "practically false," they might be defamatory, but "substantial truth" is a defense to a defamation claim, so the statements don't have to be precisely true.
If you're a well known person in the community, you might be considered a "public figure," which would mean that the press has more latitude and you'd need to prove actual malice on their part and not just negligence.
See a lawyer experienced in slander cases to fully disclose your situation, and get some specific advice.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
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