Q. Can a Cohen walk or stand underneath a tree branch by a cemetery, that is at that point less than a tefach (about 10 cm.)wide, if at the source of the branch, where it stands over a kever (grave), it is wider than a tefach?
A. Talmud (Nazir 54a) teaches that a Nazir should not walk or stand under “sechachos” which are hanging tree branches that also cover a corpse. Based on the above, Shulchan Aruch (Y.D. 369: 1) rules that a Cohen should not became contaminated by standing under a tree overhanging over a dead body, even if it is uncertain if there are branches that cover the corpse.
Shach and Taz (ibid.) explain that if the Cohen is certain that the tree he is under is not also covering the kever or the corpse, it would be permitted for him to be in its shade.
However, Horav Shlomo Miller’s Shlit’a opinion is that, in your case it may be difficult to be objective with certainty as to the real size of the branch above and the wind moving other branches towards you, so it is better for a Cohen to stay away from any tree or branch of it, when it also covers a grave.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a