Is that really the point that you took away from my comment? Let me simplify it for you:

• The law cannot possibly have a positive effect. It cannot reduce deaths no matter how effective it is because there have been no deaths.
• The law will have an outsized negative effect. It prevents and delays access to tools that are used by businesses, schools, and hobbyists. That's not even accounting for the cost to review the background checks.

This bill was just introduced, there’s little detail yet on how this could be accomplished.

Did you follow the link and read the bill? It lays it all out.

1 Section 1. The general business law is amended by adding a new section
2 398-g to read as follows:
3 § 398-g. Sale of certain three-dimensional printers. 1. Any retailer
4 of a three-dimensional printer sold in this state which is capable of
5 printing a firearm, or any components of a firearm, is required and
6 authorized to request and receive criminal history information concern-
7 ing such purchaser from the division of criminal justice services in
8 accordance with the provisions of section eight hundred forty-five-b of
9 the executive law. Access to and the use of such information shall be
10 governed by the provisions of such section. The division of criminal
11 justice services is authorized to submit fingerprints to the federal
12 bureau of investigation for a national criminal history record check.
13 2. Within fifteen business days after receiving a request for criminal
14 history information pursuant to this section, the commissioner of the
15 division of criminal justice services shall review such criminal history
16 information and determine whether such purchaser has been convicted
17 anywhere of a felony or a serious offense or who is not the subject of
18 an outstanding warrant of arrest issued upon the alleged commission of a
19 felony or serious offense which would disqualify such individual from
20 being licensed to carry or possess a firearm under section 400.00 of the
21 penal law. Such commissioner shall promptly notify the seller of his or
22 her determination in this regard. No retailer shall sell any three-di-
23 mensional printer capable of printing a firearm unless the division of
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1 criminal justice services provides written notification of the determi-
2 nation under this subdivision.
3 3. For purposes of this section, "three-dimensional printer" means a
4 computer or computer-driven machine or device capable of producing a
5 three-dimensional object from a digital model.

• Lines 3-9 - Any retailer of a 3d printer must request and receive a criminal background history for the purchaser from NY criminal justice services.
• Lines 13-22 - it will take up to 15 business days to review and provide a response.