Which country was the first to elect a female head of state?

Tannu Tuva, also known as the Tuvan People's Republic, was a short-lived and not universally recognised state that existed from 1921 to 1944 before becoming part of the Soviet Union. Khertek Anchimaa-Toka was elected as Chairwoman of the Republic in 1940 making her the first female elected head of state in the world.

https://en.wikipedia.org/wiki/Khertek_Anchimaa-Toka

Of UN-recognised states, the first was Sirimavo Bandaranaike who was elected Prime Minister of Ceylon (now Sri Lanka) in 1960.

https://en.wikipedia.org/wiki/List_of_elected_and_appointed_female_heads_of_state_and_government

Sirimavo Bandaranaike was head of government, not head of state. As the Prime Minister of Sri Lanka (then Ceylon), she served as the leader of the government from 1960 to 1965, again from 1970 to 1977, and briefly in 1994. However, the head of state in Sri Lanka at that time was the Governor-General (until 1972, when Sri Lanka became a republic and the position of President was created).

The first country to elect a female head of state was Iceland. In 1980, Vigdís Finnbogadóttir was elected President of Iceland, becoming the first woman in the world to be democratically elected as head of state. She served as President of Iceland for 16 years, from 1980 to 1996.

https://en.wikipedia.org/wiki/List_of_elected_and_appointed_female_heads_of_state_and_government