What is the biblical support for the moral-civil-ceremonial distinction of Old Testament laws?

Try http://www.christian.org.uk/wp-content/downloads/the-threefold-division-of-the-law.pdf

It explains the history of the divisions.

The following exhibit the oneness of the law biblically: For whoever keeps the whole law and yet stumbles in one point, he has become guilty of all. James 2:10 - Christ fulfilled the law. Mat 5:7 - The law is fulfilled in those that walk by the Spirit, Romans 8:4 - The law is fulfilled by loving each other, Gal 5:14

Some claim that dividing the law in three parts is "arbitrary and without any textual support." However, clear Biblical arguments have been made against this.

1. God, Himself, drew a distinction between the laws when He chose to write the moral law, the ten commandments, with His own finger (Deu 9:10), while allowing Moses to transcribe the other laws in Moses' Book of Laws.

2. Even the placement of these laws are different. The ten commandments are placed inside the ark of the covenant, under the mercy seat (Hebrew 9:4), while the Book of Law is placed beside the ark of the covenant (Deu 31:26).

3. In the same verse (Deu 31:26), the Book of Law is referred to as "a witness against you". Paul later refers to this when describing the ordinances "against us", blotted out and nailed to the cross, because it was "a shadow of things to come" (Col 2:14, 17).

4. In contrast, the ten commandments is perpetual, because it is the great law of love expanded. Love God and love your neighbour is also repeated in the New Testament. Most of the ten commandment is also repeated in the New Testament. Near the close of history, at the seventh trumpet, the Ark of the Covenant is still clearly seen in heaven (Rev 11:19).

5. Even thinking in terms of the laws before sin and the laws after sin, the distinction is clear. The moral law, the great law of love, the changeless character of God, always existed and always will be. The other set of laws, that pointed to Jesus as saviour would never have been needed when there was no sin. When Jesus died on the cross as the true lamb of God, the veil of the holiest compartment was ripped apart by God, signalling the end of ceremonies.

6. Hebrew 7:12 talks about "a change of law". The ceremonial law including the priesthood of the order of Aaron is finished (Hebrew 7:11-12). Instead, Jesus is now our high priest under the order of Melsisedec, offering only one sacrifice once and for all (Heb 9:25-26). Despite the laws in the Old Testament (Exo 29:9) requiring that Aaron and his sons be high priests forever, we now see a change of law because the first set was highly symbolic and therefore ceremonial.

Therefore, evidences are ample Biblically that there are at least two main sets of law. First type - moral in nature, based on the perpetual law of love, designed to be taken internally and written in the heart (Rev 14:12). Second type - symbolic in nature, pointed to Jesus, changed.

Because this idea is a "Christian-ese" concept that has traditionally been used to explain the heart of the Gospel with respect to the law, any answer here that Biblically explain this view will not necessarily "support this viewpoint." Much like T.U.L.I.P and the seven dispensational epochs, concepts like this tend to oversimplify Biblical truths. This doesn't mean it is unbiblical, but that it should never replace the Biblical foundation it stands on.

Moral Law: Jesus gave his own interpretation of the law in His Sermon on the Mount, but without the epistles, early Christians only had the Old Testament to deduce what part of God's commands were part of our training toward maturity (our tutor in Gal. 3:24), and what parts reflect the Law of Liberty in Christ (Rom 8:2). Jesus' revelationary [sic] contribution to our understanding of Moses' law tells us that we are not to disregard it completely, but we need to discern which parts of the law were established for our "upbringing," and which they would have to preserve in their new life with Christ. When Jesus said "You know the commandments" to the rich young ruler in Mar 10:19, he was likely talking about the Ten commandments, or more broadly, the "Moral Law" of Moses. Even with our death to the law (see Rom. 7:4), our obligation to be like Christ does not change. The Prophet David says in Psa 40:6 "Burnt offering and sin offering You did not require," but this sounds contradictory since God literally did require it in Moses' law. But not forever. This example is a good distinction between where Moses' law and the Law of Liberty separate. God calls David a man after His own heart probably in part because he saw the difference. Other verses like this exist. See Micah 6:8:

He has shown you, O man, what is good; And what does the LORD require of you But to do justly, To love mercy, And to walk humbly with your God?

So, the "Moral Law" in our simplified tri-part system we're examining here are any of those commands about which David could not have said "you did not require." Most of these "required" laws, based on our David definition have a broader "Law-of-Liberty" version: Hate is murder (Matt. 5:22), idolatry is covetousness (Col. 3:5), but, as always, God's heart doesn't change.

Ceremonial Law The letter to the Hebrews (especially chapter nine) reveals that much of Moses' law contained copies or patterns of heavenly truths. Just as there is an altar in Moses' law, there is a version of that in heaven, from the Priesthood, down to the altar and candles. These patterns given to us in Moses are "Shadows of the good things to come" (Heb 10:1), so they are similar to the Moral Laws in that they reveal a bigger truth. In this case however, the truths they reveal are not mandates of holiness. They are symbols of heavenly places. So the "Ceremonial Law" in our simplified tri-part system, are any commands about which David could have said "you did not require," and were shadows of things to come, and were not primarily commands for civic functions. Not all these are in Hebrews, but it gives us a good starting point.

Civil Law By process of elimination, I would say that these commands are those which do not adequately fit in the categories above, but, like your question states, called the Hebrew people to form a working society. In my opinion, it's really hard to separate this category from the Ceremonial Law without adequately defining "Civil" and "Ceremonial." Especially in a society where law and faith are never separated. Laws that talk about inheritance, land boundaries, and punishment for crime, might nicely fit here, but couldn't someone also say they point to shadows of things to come, i.e., the judgement and reward of God's people and enemies? Maybe, but again, this three-fold division is never explicitly made in the scriptures.