Generally filing a police report will suffice, if I’m not mistaken. Could you lie? Of course, but (1) it’s generally not in your best interest because the insurer might raise your rates and/or discontinue coverage, and (2) you’d be making a decision to make false statements to the police for purpose of fraud, which most reasonable people won’t do.
Other than perhaps using cameras as a means to deter thieves, I’m not sure that low-value (under USD 5000) items like bicycles are worth the time and effort for insurers to launch full investigations over.
