Let's say he is speaking to the Jews (we are still debating whom he is speaking to).
Hold on...let's not make that assumption. The letter is to the Roman believers, who were made up by both Jew and Gentile.
.... Paul is saying that they died to the law, or were released from the law or were no longer under the authority of the law, what law did he mean?
Let me use you to answer the question.
When
you sin (and you do sin) the law can't condemn you. Why you have been delivered from under its demands, i.e., "obey and live, disobey and die". It can't place you in death row. Why? Two reasons:
1] The justice of the law has been satisfied because your "old life" (which we still need to iron out) died in Christ. Thus as far as the law is concerned, you are dead.
2] The law is satisfied with your "new creation" that is "in Christ" in the heavenly places because that humanity is immortal and sinless. That's because Christ was resurrected with a glorified humanity, free from sin. That humanity (your new creation) Christ took to heaven when He was resurrected (see Eph 2:6 & Col 1:13). So in Christ the law sees you as you are "in Christ".
This is good news to sinners, but bad news to the legalist among us....