The District of Columbia actually has the most people per square mile at 11,011 but its not a state, making New Jersey the most densely populated state.

New Jersey with 1,218 people per square mile, edges out Rhode Island which has 1,021 people per square mile.

People might consider New York with it's massive NYC population to be the most populated state but it comes in 7th with only 420 people per square mile.

New Jersey has a total population of 8,958,013 and it has a land mass of 7,417 square miles as of a 2015 survey.

More Info: en.wikipedia.org