Question
Was there a process of impeachment if a king was found to be in violation of dharma?
Answer
No such thing as impeachment is found in the Smritis. But I've found something relevant in the Mahanirvana Tantra's 11th Chapter, which talks about Prayaschittas (expiatory rites), regarding what shall be the punishment for such a King.
[Lord Shiva says] O Kula−nayika! know that there are two kinds of sin−− that which contributes merely to the injury of one's own self, and that which causes injury to others (15). Man is released of the sin of injuring others by the punishment inflicted by the King, and from other sins by expiatory rites and Samadhi (16). Those sinful men who are not purified by either punishment or expiation cannot but go to hell, and are despised both in this world and the next (17). O Adya! I shall first of all speak of the Rules relating, O Maheshvari! to punishment by the King. The King who deviates from these himself goes upon the downward path (18). In the administration of justice, servants, sons, mendicants, friends, and foes should all be treated alike (19)
If the King is guilty of any sin himself, or if he should have wronged one who is not guilty, then he may purify himself by fasting and by placating those he has wronged by gifts (20). If the King should consider that he is guilty of any sin which is punishable by death, he should then abdicate his kingdom and go to a forest, and there labour for his liberation and penances (21). The King should not, without sufficient reason, inflict heavy punishment on persons guilty of a light offence, nor should he inflict light punishment on persons guilty of a great offence (22). But the punishment by which many offenders may be deterred from ill−doing, and (punishment) in the case of an offender who is fearless of crimes, should be heavy, although the offence be a light one (23).
So, the King has to punish himself. If he does not do that then that takes him downward, but that's in afterlife.
I have found no mentions of an impeachment.
UPDATE:
Similar verses, like the ones given above, are also found in Vashishta DharmaSutras' Chapter 17.
By failing to inflict punishment on a thief, on a cursed wight, on a wicked person, on one [caught] with weapons in his hands, on a thief caught with stolen property in his possession, on one covered with wounds and a cheat, a king shall fast for one night ; and the priest, for three nights. If an innocent man is punished [the king shall perform] a Kricchacha penance, and the priest [shall fast] for three nights.
And, from the 18th Chapter of the same Smriti:
THERE is penance for a crime committed unwittingly ; some [say] also for [a crime] committed intentionally. The spiritual teacher corrects the learned; the king corrects the evil-minded, but Yama, the son of Vivasvat, indeed punishes those, who commit sins secretly.
So, a king, who himself is guilty, has two options - either he has to do the prescribed penances or get punished by Yama in afterlife. The subjects can not overthrow him or question him it seems.
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