First of all you may only kill a tree if it is yours and it is not protected by a tree preservation order (TPO) or in a conservation area. If you harm a protected tree and you are caught,the fines are severe,believe me. So given that it's your tree and you are allowed to fell it then call some registered tree surgeons and get some prices. It's the safest way of sealing with it. If you just kill it,it will still be there only dead and the dead branches will eventually break off in the wind and could hurt/kill someone. If the tree is less than,say,15ft tall you will be able to safely kill it by cutting a ring of bark off the tree 6" wide around the circumference as low to the ground as possible.