Q. Since you also wash after bloodletting, does that mean that you have to wash after a blood test? Or does a surgeon wash 3 times after an operation?

A. See prior question in regards to washing three times. Shulchan Aruch (O.H. 4: 19) advises to wash hands after bloodletting. Mishna Berura (4: 48) recommends washing after applying leeches or “bankes”. However Nishmas Avrohom (4: 4) quotes Horav S. Z. Auerbach’s Zt”l decision that after extracting blood for an analysis or even when donating blood, no hand washing is required. The reason given is that this washing requisite is of “segulaty” origin or of spiritual nature and not a medical need. As such we should limit it only to its original provision and that is when the blood was drawn as a healing practice. We do not require it when the blood extraction was done for any other reason such as testing or for helping others by donating blood. (see Ishei Yisroel 2: 41: 149 and Piskey Teshuvos 4: 27).

Following this reasoning we may require the surgeon to wash hands after an operation, since that could be seen as a healing procedure. The fact that the surgeon wears gloves may be of no consequence, as a sleeping person wearing gloves also washes when he awakens. (ibid.) However, this is not the accepted custom.

Sha’arey Aharon (4: 19) remains doubtful whether you require hand washing after drawing blood for a medical analysis. Some Poskim suggest that it is proper to wash (Piskey Teshuvos 4: 27 quoting Leket Hakemach)

Horav Shlomo Miller’s Shlit”a opinion is that you don’t have to wash “netilat yadaim” after  donating blood, a blood test, or an operation.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a