Currently, there are no states where it's legal for a non-citizen to vote in a federal election.
The question is whether all states' laws specify that proof of citizenship is require for voter registration. I would tend to assume that in each state, the law would require that in order to register to vote in a federal election,
- the person must present an official document that is proof of citizenship, such as a US birth certificate or US passport, at the time of registration, or
- the person's citizenship status must be verified by looking it up in some database that required proof of citizenship. (For example, the Social Security Administration keeps a record of whether a person is a citizen, and this requires proof of citizenship to be presented to the SSA office.) Or,
- in cases where the above two conditions are not satisfied, the person will receive a limited voter registration record that is only valid for state and local elections (in the case of states that allow non-citizens to vote in such elections), and such a person would only be able to obtain a limited ballot without any federal candidates on it (see https://law.stackexchange.com/a/46455/765).
Are there any states where such legal provisions to prevent non-citizen voting do not exist?