First, Paul used the term "died with Christ" to refer to baptism, and the author of Colossians follows Paul's meaning closely here. For example:
Romans 6:2-4: God forbid. How shall we, that are dead to sin, live any longer therein? Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
Most Bibles translate στοιχείων as 'principles', which may camouflage our author's real meaning. Perhaps a better translation is 'rudiments' or 'elements', with reference to the every day things of no lasting importance.
Colossians is saying that rules like ""Do not handle! Do not taste! Do not touch!" were written for the unbaptised, but if you have died in Christ (having been baptised) then they no longer apply.
At this stage, perhaps the KJV happens to be a clearer translation:
Colossians 2:20-23: Wherefore if ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to ordinances, 21(Touch not; taste not; handle not; 22Which all are to perish with the using;) after the commandments and doctrines of men? 23Which things have indeed a shew of wisdom in will worship, and humility, and neglecting of the body; not in any honour to the satisfying of the flesh.
The essence of the question is in verse 22, which Christopher R. Seitz (Colossians (Brazos Theological Commentary on the Bible) says is "so sufficiently compressed that it is difficult to perceive the meaning."
Although this may rest uneasily alongside the Old Testament, verse 2:22 can perhaps be read as saying that these rules came from men, but this seems by no means an indisputable interpretation. In any case, John Gill gets around this ambiguity by saying that the laws originally came from God, but that the imposition of the law comes from man (if that makes sense):
... even the ceremonial law, being now abolished, originally of God, yet the imposition of it, as necessary to salvation, was a commandment and doctrine of man's; and particularly the traditions of the elders, and the various rules and decrees, which the doctors among the Jews obliged men to regard, were human inventions and devices.
On the other hand, Barnes' Notes to Colossians 2 says that "these ordinances had a value among the Hebrews when it was designed to keep them as a distinct people; but they had no value in themselves, so as to make them binding on all mankind," going on to say, "They depended on human authority only, and of course, should not bind the conscience."
This takes us back to Seitz' comment that it is difficult to perceive the meaning of this verse. For the author, the meaning of this clause may not have been important, as long as it paralleled the words he believed Paul might have used. Whether verse 22 implies that the Jewish law was originally of God or were simply of human origin is subject to debate.