I am a claim advocate with 40 yrs experience having worked for the nation's largest insurers from California to Florida. Theft claims are the toughest to settle as there is usually little proof of the loss values and the goods are subject to over exaggeration, even if you have photos before the loss. Insurers hate theft claims and try to deny most unless you catch the culprit.
There are many nuances involved in a theft claim. Your first duty is to file a police report and then all available proof of purchases if they were not also stolen. You did the right things it sounds like. Giving a statement is a way to get the facts, but many adjusters use it to entrap you into misrepresentations so it looks like you stole your own goods. Thefts become very adversarial as they first suspect your lying to them. They can only assume your guilty.
The State does have strict standards to follow in a denial process which requires them to detail out the problem areas as well as the policy provisions they are relying upon. They may also require an Exam under Oath and also for you to file a Proof of Loss within 60 days. Simply at that point, they are looking to deny your claim.
You can contact the California Dept of Insurance for assistance and let them investigate for flaws in CNA claim protocols. If you have cooperated fully and given them everything you have in your possession, they cannot expect more of you. If you fail to cooperate then they can deny your claim on those grounds. Contact the insurance Dept and file a complaint by internet or over the phone at :
www.insurance.ca.gov/contact-us/ and go to "file a complaint" or call them at
800 927 4357.
You can also consult with a Claim Advocate/Public Adjuster in your area for free advice....
The Claim Advovcate