Under the Mosaic Covenant, an autopsy would be not be impossible, but the person touching the dead body would be unclean for seven days.
He who touches the dead body of any person shall be unclean seven days.(Numbers 19:11)
Some people may think that the prohibition to make markings on one’s body might also prevent an autopsy.
You shall not make any cuttings in your flesh on account of the dead or tattoo any marks upon you: I am the Lord. (Leviticus 19:28)
The prohibition regarding cutting one’s body concerns the dead. Tattoos on behalf of the dead are not permitted, nor is scarring. Scarring obviously requires cuts, whereas tattooing can be done with needles and pigment. However, even tattooing appears to have the same consideration as scarring because the needle has to penetrate the skin.
The difference between the Mosaic Covenant and the Kingdom of God: the former has to do with this Earth; the latter has to do with eternity.
When Jesus spoke about leaving the dead to bury the dead, this has to be understood in the context of God’s purpose.
But he said to him, “Leave the dead to bury their own dead; but as for you, go and proclaim the kingdom of God.” Luke 9:60
The purpose of God is to call all men to a better hope other than merely being born to die. However, the prohibitions that were associated with the Mosaic Covenant are of no effect today—but this does not include the moral covenant of the Ten Commandments written by God’s Own Finger (Exodus 31:18).
Now the Kingdom of God is proclaimed and the message is that God’s grace is sufficient for us to exercise faith in the resurrection; for the requirements of the Mosaic covenant were of no effect; merely being a body of knowledge that provided instruction about salvation. Therefore, what medical science has to offer, and what the individual government authorities of the world may require, have no effect upon the born again believer, unless the believer is being forced to deny Lord Jesus Christ or transgress the commandments of God.
No one who denies the Son has the Father. He who confesses the Son has the Father also. Let what you heard from the beginning abide in you. If what you heard from the beginning abides in you, then you will abide in the Son and in the Father. And this is what he has promised us, eternal life. (1 John 2:23–25)
And by this we may be sure that we know him, if we keep his commandments. He who says “I know him” but disobeys his commandments is a liar, and the truth is not in him. (1 John 2:3–4)
From a New Testament perspective, the Mosaic Covenant is not required to be kept. The Mosaic Covenant is different from the only words written by the Finger of God. These the Christian is now capable of keeping because they ought to be second nature to a person who has been baptized in the Holy Spirit.
The moral code is separate to the Mosaic Covenant (or Code), because it applies to everyone. The Mosaic Covenant only applied to those who had been rescued from Egypt and their descendants according to the flesh up until the time of the outpouring of the Holy Spirit at Pentecost. Since Pentecost, the New Covenant of life in the Spirit of God has been instituted.
Those who perform autopsies are seeking to establish reasons for a person’s death, for human governmental purposes that have to do with this world; it is difficult to see how this affects a Christian.
The Apostle Paul does say that Christians are to be subject to human government (Romans 13:11).This comes with the proviso that Lord Jesus Christ is not denied and moral law of God is not contravened.