not an accurate statement.
Crime rates are difficult to clearly discuss. Generally, crime is down in NYC. Simply speaking, It is just harder to be a victim of a crime if you are not leaving your house much. Murder is definitely up. However, it is difficult to tell who is getting murdered. Since you are most likely be murdered by someone you know, I don't think this is representative of a general danger of getting killed. My concern is domestic abuse is likely the culprit here. Finally, crimes related to burglary are up but this is primarily non-residential. So much commercial property was barely being used that it was an easy target. Skyrocketing crime rate is not an accurate description and it is especially not accurate when assessing one's potential to be a victim of a crime.
NYC was also doing very well for a large US city with covid after the initial wave. However, there has been a bit of a resurgence recently. My hunch is that it is due to the High Holy Holidays and will continue the downward trend again soon.
Sorry if I am being nitpicky but I am hearing a lot about NYC that isn't accurate and is being used to support political/ideological/social views.