Under the us constitution could both national and state governments conduct elections?

Yes. Under the U.S. Constitution, both the national and state governments can conduct elections. The Constitution gives the states the power to regulate elections for federal offices, but Congress has the power to make or alter regulations for such elections. This means that states have the primary responsibility for conducting elections, but Congress can set rules governing how those elections are conducted.

For example, the Constitution requires that each state hold elections for members of the U.S. House of Representatives and the U.S. Senate. The states are responsible for setting the date and time of these elections, as well as the qualifications for voting. However, Congress has passed laws that set minimum standards for voter qualifications, such as requiring that voters be at least 18 years old and U.S. citizens.

The Constitution also gives the states the power to hold elections for state and local offices. States have the full power and responsibility for conducting these elections, including setting the dates and times of elections, determining voter qualifications, and counting the votes.

So, while the national government does have some power to set rules for federal elections, the states are the primary entities responsible for conducting elections in the United States.