The law sounds like the federal requirement for mail-in registration under the Help America Vote Act codified as 48 USC Section 15483.
§15483. Computerized statewide voter registration list requirements and requirements for voters who register by mail
(b) Requirements for voters who register by mail
(1) In general
Notwithstanding section 6(c) of the National Voter Registration Act of 1993 (42 U.S.C. 1973gg–4(c)) and subject to paragraph (3), a State shall, in a uniform and nondiscriminatory manner, require an individual to meet the requirements of paragraph (2) if-
(A) the individual registered to vote in a jurisdiction by mail; and
(B)(i) the individual has not previously voted in an election for Federal office in the State; or
(ii) the individual has not previously voted in such an election in the jurisdiction and the jurisdiction is located in a State that does not have a computerized list that complies with the requirements of subsection (a) of this section.
(2) Requirements
(A) In general
An individual meets the requirements of this paragraph if the individual-
(i) in the case of an individual who votes in person-
(I) presents to the appropriate State or local election official a current and valid photo identification; or
(II) presents to the appropriate State or local election official a copy of a current utility bill, bank statement, government check, paycheck, or other government document that shows the name and address of the voter; or
(ii) in the case of an individual who votes by mail, submits with the ballot-
(I) a copy of a current and valid photo identification; or
(II) a copy of a current utility bill, bank statement, government check, paycheck, or other government document that shows the name and address of the voter.
https://www.justice.gov/crt/chapter-146-election-administration-improvement