Hints at what Micah had in mind may be found in the Books of Kings.
Joseph Blenkinsopp, A History of Prophecy in Israel, page 115:
The allusion to "statutes of Omri" and "deeds of Ahab" (Micah 6:16 recalls the condemnation of Manasseh for imitating the much-maligned Ahab in setting up syncretist cults (2 Kings 21:3; cf. 23:4-14). Micah 6:9-16 also parallels Zephaniah in several respects. Both condemn an unnamed city, which must be Jerusalem (Micah 6:9; Zeph. 3:1), and expatiate on the evils of idolatry in general and the cult of Baal in particular.
The text of 2 Kings 21.3 reads:
For he rebuilt the high places that his father Hezekiah had destroyed; he erected altars for Baal, made a sacred pole, as King Ahab of Israel had done, worshipped all the host of heaven, and served them.
The other text, 2 Kings 23.4-14, describes how ritual objects for Baal and Asherah worship were removed from Jerusalem's temple at a later time.
Micah may or may not have in mind a specific written set of laws from Omri (à la the Code of Hammurabi). The parallelism with 'the works of the house of Ahab' suggests the prophet is referring to a general swath of practices and customs enforced by Omri, Ahab, and their dynasty, practices and customs which consist of worshiping gods alongside or above Yahweh.