A Kohen who has taken a life may not bless the nation, as it is written (Isaiah 1:15), “When you spread your hands [in prayer], I will turn My eyes away from you… [for] your hands are full of blood” (Berachot 32b). This means that only hands clean of blood are kosher for reciting Birkat Kohanim. This is similar to a sacrificial altar, whose stones are forbidden to be shaped using iron, since iron shortens human life, whereas the altar is intended to make peace and lengthen human life. Similarly, a Kohen whose hands have been contaminated by blood may not bless the people and bestow abundant blessing and peace upon Israel. The task of the Kohen is to augment kindness and life, like Aharon HaKohen, who was a lover and pursuer of peace, and a Kohen who has killed has damaged the core of his priesthood.
According to the Shulchan Aruch (Orach Chaim 128:35), no repentance can help a Kohen who has committed murder. Even if he killed accidentally, repentance will not do him any good, since a prosecutor cannot become a defender, and hands that have committed murder are forever ineligible to bestow Birkat Kohanim upon the nation.
However, according to the Rama, if the Kohen fully repents and goes to a sage who will arrange a process consisting of fasting, giving tzedakah, and accepting upon himself not to sin again in the future, then after concluding the process of repentance, he may resume blessing the people. Someone who repents becomes a new person, and therefore, even if he committed murder intentionally, if he completely repents, he may resume blessing the people.
There is an intermediate opinion which maintains that a Kohen who murdered accidentally and repented may bless the people. However, a Kohen who intentionally murdered someone may not bless the nation even after he repents (Pri Chadash; Eliyah Rabbah; Bei’ur Halachah 128:35). A Kohen who experiences such a serious incident must go to his rabbi to receive personal advice regarding how to practice.
Similarly, a Kohen who has unintentionally run over and killed someone with his car may not ascend the duchan for Birkat Kohanim. As mentioned previously, the poskim disagree as to whether repentance would be effective. However, if there was no negligence on his part while driving – for example, a child suddenly jumped under the wheels of his car and he could not prevent the accident – then in such a case, he is not even considered one who kills unintentionally. Rather, he is seen as a person who killed due to circumstances beyond his control, and according to all opinions, if he repents according to the instructions of his rabbi, he is permitted afterwards to resume blessing the nation (Yechaveh Da’at 5:16).