What should I do if I am being threatened on Twitter?

[Kasper]

Assess the likeliness that the owner of said twitter account will indeed follow up on his/her alleged threats. Are you traceable towards your address by the data provided by your twitter account? If yes, you might want to secure that by deleting said data.
As for the threat itself, in most cases words are just words on the internet and rarely will people actually follow up on their threats, lest there is a very strong reason to do so. Language is very much subject to deflation and inflation on the net, in such a stron notion that meanings of things might very well change.
Every day thousands of death threats are flung across the internet, whereas very few actually get carried out.
As to the threat of kidnapping, that would not help the perpetrator at all, as his/her intention was to hurt you, which he succeeded at, clearly, but kidnapping does not happen with an advance announcement. That is just plain stupid and the person who threatened you knows it. Announcing to someone he will be kidnapped is a great act of stupidity if actually intended, so the only possible outlet would be that this threat was just words, no intention to follow up on anything.