It is an American Entertainment Industry misconception that victims (or anyone else) have the ability to tell the police or the prosecutors how and when to do their jobs.
Hypothetically, a private homeowner could choose not to report a break-in as a crime, since it wasn't violent, and it wasn't commercial property, and if the crooks are not gangstas or some other group-backed actor, then they could quietly put the crime to rest. This would also be a question of the insurance company's policy.
But if there were a crime that did damage, usually there is a question that comes up in the police report like, "as a victim, are you prepared to cooperate in the investigation?" and if you do not tick "yes" then you can probably count on nothing else being done whatsoever.
https://www.maricopa.gov/911/Remain-Silent
https://www.ajblawfirm.com/articles/understanding-pressing-c...