Here is some brief information from Publication 547 (publications are not tax law but are general basic guides):
"Theft loss proof.
For a theft loss, you should be able to show all of the following.
When you discovered that your property was missing.
That your property was stolen.
That you were the owner of the property.
Whether a claim for reimbursement exists for which there is a reasonable expectation of recovery.
It is important that you have records that will prove your deduction. If you don't have the actual records to support your deduction, you can use other satisfactory evidence to support it."
More information:
"Theft" losses are generally reported on Form 4684 https://www.irs.gov/pub/irs-pdf/f4684.pdf
"Capital" losses are generally reported on Schedule D https://www.irs.gov/pub/irs-pdf/f1040sd.pdf