I had this before and the police did bot bugger all. The didn't even log it as a crime.
I spoke to the guy last night at 10pm. At 11.30 he rang again but I missed the call. I rang it back this morning and spoke to a different guy who said he had lent the phone to his mate in the pub last night.
I have the number, they didn't even bother to hide it.
Try getting a crime number from them to ensure it is logged. If the copper on the front desk won't log it, (politely) say that you wish to report this crime to someone of higher rank. If the copper on the desk still won't do anything, write in with your report to someone of higher rank, expressing the fact that you are prepared to go to someone even higher if the crime is not logged. I'm sure that many coppers are OK but unfortunately, some of them can't be bothered with the paperwork unless there is a good chance of nicking someone.
Although a threat to kill in anger is very rarely acted upon, it is regarded as a serious offence (unless the copper is the gun holder in which case they are allowed to shoot a person with table leg in a bag and pull naked a unarmed man out of bed and kill him with, apparently, the full backing of the state).