Ex husband jealous of my new boyfriend?

My ex husband and I have been apart now for 3 years going on 4. Our divorce has been final and we have lived separate since. We have a mutual child together. My ex is a cop, part of our split was infidelity. Even now to this day many people are telling me often how he is involved with different women. The reason they are telling me is because he a little while ago professed that he wanted to get back with me but is seeing so many other people. I have been dating a guy for a little while and we have gotten pretty close. I informed my ex that I am seeing someone because he kept trying to make passes to me. He has now out of jealousy began threatening me that if my new beau comes around our son that he will try and kill him(the boyfriend). In the position he holds as a police officer, I would hope he wasn't like that. My boyfriend does nothing wrong to my son, nothing but have fun with him and show him how a man is suppose to be. My ex, his father, spends little to no time with him and is getting jealous of the fact that my son does like my boyfriend. I just don't know what to do as far as his jealousy is concerned. I don't know how serious to take his threats nor how to handle the situation. I just know that I love my boyfriend and I don't want anything like a stupid ex to cause much problem. Just need some advice.