In my day job I am a cop so I am understand both sides of this story. I have worked in almost all the capacities I will be detailing here, a dispatcher, a street cop, and an investigator. Here are some tips for everyone to get a little more responsiveness from cops as they show up. Now these tips may or may not work. As with any crime, you need to be able to prove who did it. A lot of times this is impossible because you did not witness your tenant actually steal or destroy your property. This is why in almost all cases it is a civil matter, not criminal. The reason it is civil is because the tenant is entrusted for the care of the property during their lease according to the contract. So while you can easily prove responsibility, it is a much harder thing to prove guilt of the crime. Think OJ, not guilty of the crime, but found responsible for it.
First get familiar with the sections of law that pertain to Theft, Grand Theft, and Burglary. There are websites where you can search your laws, usually it is all in the penal code (CA website is http://leginfo.legislature.ca.gov/faces/showCodesTextSearchResults.xhtml a good search term is “find (your state) code”). Theft and Grand Theft are basically the same, but the dollar amount is different (in CA Grand theft is anything over $950). Burglary is basically entering a structure and taking anything no matter the cost (at least in CA it is). So once you have this knowledge you are more prepared to call the cops and get past the first screening from the dispatcher. Realize in most cases the dispatcher answering the phone and sending the police to your location is a civilian with much less training than the cop coming to your house. When it is a landlord tenant issue they will usually only come out and keep the peace because most calls they do get are for civil matters that only can be handled in a court. But if you call to report a theft, or burglary, there is no question it is a criminal matter.
Second, when the cops do show up, be prepared to wait, because it is not a high risk priority, have all the information ready for them. All the recruiting video I see put out by different agencies show the fun and exciting part of the job, but most of our day is filled with writing reports, this is extremely boring and as you can guess, a lot of cops try to get out of writing a report if they can convince the person they are dealing with it is a civil issue. So they way to be prepared is to have a report already typed or written up explaining the circumstances, property stolen and/or damaged with the costs and serial numbers if you have them in the case of them being stolen, and any opinions you may have to lead the detectives in a direction. Cops cannot put their opinions in a report, only fact. Things that will help a lot are any neighbors that saw them loading the property into their vehicle or witnesses to them taking a hammer to your walls. I personally plan on having a $300-$400 camera system that monitors the exterior of the building that will record a month of activity. I also plan to do monthly inspections of my properties so that if something does happen, I still have it on the camera system. Things that would prove guilt in a criminal court. Some agencies without this type of information may not take a report.
Third is the Detective. He/she has to prove reasonable suspicion that the person committed the crime you allege. Like I said earlier this is done by witnesses and or video. Once the detective has enough information they can go to the district/city attorney to file criminal charges against the suspect and get an arrest warrant. If you get this far, plan on coming to court to testify, you would not believe how many people go free because the victim does not come to court.
Final tip, if you truly believe that the cop or detective is not doing their job ask for the supervisor. Field cops will always have a supervisor available to come to you. Hope this helps.