Most of the direction from the branch is regarding child sexual abuse. The elder's manual states:
ks10 pg 38
20. If the sin occurred before he was appointed as an elder or a ministerial servant, the elders will need to take into consideration the fact that he should have mentioned this possible impediment to his being qualified when elders interviewed him just prior to announcing his appointment. Moreover, the nature of the sin may reflect greatly on his qualifications to serve. For example, the sin may involve past child abuse, and this would likely disqualify him for many years.—w97 1/1 pp. 26-29; w77 pp. 697-698.
And the most recent letter regarding child abuse states:
15. Who is considered a known child molester? The January 1, 1997, Watchtower article “Let Us Abhor What Is Wicked” mentions on page 29 that a man “known to have been a child molester” does not qualify for privileges in the congregation. The expression “known to have been a child molester” has reference to how such a man is considered in the community and in the Christian congregation. In the eyes of the congregation, an adult “known” to be a former child molester is not “free from accusation” or “irreprehensible,” nor does he have “a fine testimony from people on the outside.” (1 Tim. 3:1-7, 10; 5:22; Titus 1:7) In view of his past, those in the community would not respect him and congregation members might be stumbled over his appointment. Keep in mind that the branch office, not the local body of elders, determines whether one who has sexually abused a child is considered a known child molester.
22. It cannot be said in every case that one who has sexually abused a child could never qualify for privileges of service in the congregation. However, the elders will certainly want to be very cautious, especially when dealing with one who had repeatedly engaged in this kind of wrongdoing or who had been disfellowshipped for such an offense. Before privileges can be extended, such a man must meet the Scriptural qualifications of being “self-controlled” and “irreprehensible.” He must “also have a fine testimony” from individuals inside and outside the congregation. (Titus 1:6-8; 1 Tim. 3:2, 7) Elders should keep in mind what is stated in the Re: Child abuse October 1, 2012 Page 6 January 1, 1997, Watchtower article “Let Us Abhor What Is Wicked,” page 29, paragraph 2: “Child sexual abuse reveals an unnatural fleshly weakness. Experience has shown that such an adult may well molest other children. True, not every child molester repeats the sin, but many do. And the congregation cannot read hearts to tell who is and who is not liable to molest children again. (Jeremiah 17:9) Hence, Paul’s counsel to Timothy applies with special force in the case of baptized adults who have molested children: ‘Never lay your hands hastily upon any man; neither be a sharer in the sins of others.’ (1 Timothy 5:22).”
23. Hence, privileges of service should never be extended hastily. Considerable time should always pass before one who has sexually abused a child is recommended, if ever. It would be up to the local body of elders to determine whether such a recommendation should be made to the branch office, taking into account all factors in each individual case. Please note that unless specifically approved by the branch office, one who has sexually abused a child should not be used to conduct any meetings held in the congregation or in a prison, and he does not qualify to work on any Kingdom Hall project other than one involving the congregation where he serves as a publisher.