You should first consult with an attorney before making any statement to the police, much less handling over incriminating evidence. I'd rather keep the option open to fight over it in court than just giving up the key and hoping that the police will view it in my favor. Also, encryption is a must in case of theft.
Sometimes saying anything at all might incriminate you because you're the only suspect. Don't talk to cops without a lawyer basically is the way to go in the USA.
In Japan, you are currently allowed a lawyer to be present when being questioned, but it wasn't that long ago that you weren't. However, there was a bit of a hack: you were guaranteed to have a translator. It didn't matter how good your Japanese language skills were, you could demand a translator (assuming you spoke another language!) and they had to be present during all interrogation. While not as good as a lawyer, at least you had a witness if something untoward happened during the interrogation (which was apparently quite common in those times). I have heard that since the latest reforms in the last 10 years (lawyers present during questioning and allowance of a trial by jury) the incidence of untoward occurrences has decreased. While police here are an extremely friendly feature in society (very different than any other country I've lived in), you definitely don't want to get on the wrong side of the law one way or the other.
