Constitutionally, the responsibility (and right) lies with the state legislators. This right was removed by some states' governors usurping that authority and granting it to the particular Secretary of State . I imagine the state legislatures would still have the power to carry out their duty if fraud was proven to them.
https://www.americanthinker.com/articles/2020/11/the_founders_outsmarted_the_presidential_election_fraudsters.html
Constitutionally, the responsibility (and right) lies with the state legislators. This right was removed by some states' governors usurping that authority and granting it to the particular Secretary of State . I imagine the state legislatures would still have the power to carry out their duty if fraud was proven to them.