Under Carrie Chapman Catt's leadership, what was one method used by the National American Woman Suffrage Association (NAWSA) to promote suffrage for women?

NAWSA used the referendum process to try to pass state suffrage laws.

Explanation:

Carrie Chapman Catt was American leader who campaigned for the nineteenth amendment to the US constitution. This amendment denies the federal government from denying the right to vote to the citizens on basis of sex. It was passed on 4th June 1919.

She twice served as the president of the National American Woman suffrage Association and the women in US got the voting rights due to her efforts. She became involved in the women suffrage movement in 1880's and organised campaigns and mobilised volunteers for the cause.