It does.
The U.S. Constitution, Article Four, Section Four
"The United States shall guarantee to every State in this Union a Republican Form of Government..."
In other words, a form of state government that conforms to the model of our national government.
And, one that is based on the same bedrock principles.
This is not optional.
The Fourteenth Amendment clarified this even further.
Not saying that I agree with this... However, unfortunately, the Supreme Court has interpreted the Republican Form of Government Clause inherantly involving political questions and therefore nonjusticiable. In other words- they have for all intents and purposes written it out of the Constitution.