This is what wikipedia says
In 1931, the Dominican Feminist Action, led by Abigail Mejia, hosted the First Feminist movement in the country demanding equal rights under the Constitution. Dominican women won the right to vote in 1942, through the constitutional reform of that year, which were established in Articles 9 and 10. This marked an important civil and political change of women's rights in the Dominican Republic. The progressive policies implemented by the government of Juan Bosch in 1963 allowed women to begin to organize their grassroots movements at different levels of society.
Decades later, in the early 90s, women's organizations in the Dominican Republic began to demand greater inclusion in elections. In that sense, the first female quota law was enacted on December 21, 1997, which established that at least 25 percent of candidatures for elective positions of the parties would be occupied by women. Subsequently, this percentage was raised to 33 percent. These laws set aside a minimum of candidates for elective office for women.
I know that in the municipal elections if the mayor is male the deputy major has to be female and vice versa.