Ex troubles!?

my sisters and her ex broke up about two weeks ago! she doesnt love him anymore, and wants things to end, trouble is he cant let go! he texts her and phones constantly! at first she was sympathetic but now it's ridiculous, he gets nasty and calls her all the names under the sun and has started threatening her with violence and slander ect"! she has done nothing to him except reject him i guess! when we ignore him and block contact he starts to ring anyone who knows her, and we're getting concerned that this might spiral out of control! we will call police if we have to, but i'm not sure if they will get involved, what do you think? can they at least give him a warning? he hasn't been physical with her yet!