There's no easy way to say it - there has been an increase in crime against tourists over the past few years in Costa Rica.

It is, however, mostly opportunistic theft of personal belongings with items such as passports and travel documents being the main problem. There has also been a marked increase of violent crime against tourists with gang muggings and armed robberies occurring even in daylight on busy streets. Travellers are advised to maintain at least the same level of personal security they would anywhere else in world.

It's advisable to wear a money belt, and never carry anything of value in an outside pocket; it is also wise not to wear jewelry or carry expensive equipment, such as cameras while walking around downtown.
Travellers are urged to be vigilant and be cautious in unfamiliar areas, only take proper licensed taxis. Official taxis are red with a triangular sticker and plastic box on the roof with the name and number of the taxi company.

I hope this information proves helpful!