Tell the Police
If you’re the victim of a crime in Costa Rica you should report it to the local police. You’ll need the report for insurance, credit card coverage (VISA signature will replace anything stolen in the first 90 days after purchase), or at least so you can claim the theft loss deduction on your taxes.
Of course if your passport is stolen you’ll have to travel to San Jose (Escazu) to report it to the embassy and obtain a replacement before you can return home.
Theft victims commonly report that the local police make excuses about the report officer not being around, try to convince the victims that they lost their possessions or flatly refused to make or file paperwork. The statistics from the embassy back this up showing less than half of the missing passports show up in official police reports. Be persistent and get everything in writing (even the excuses if that’s all you’re getting).
Preventing crime reporting has obvious political and economic benefits. First the local constabulary gets credit for doing a good job because crime is down, and second the national government and tourism board avoids embarrassing costly negative publicity.
If you’re polite, persistent, and insistent then make a point of writing down the officers names on a scrap of paper eventually you’ll get a copy of a report (but don’t be surprised if the original goes straight into the round file).
The one time I had to get a report I was given the original. There wasn’t even a pretext of making a copy for police department use in investigating the crime.
Tell the Hotel or Tour Operator
Hotels lodges and tour operators may well do more for you than the police. Their livelihood depends on Costa Rica’s reputation and their reputation as safe, fun and happy. Some of the more modern resorts have magnetic key card entry and logs of when maids or others are in and out of your room and they have been known to actually track down robbers.