At the end of the tenth century, Pisa was still nominally part of the Holy Roman Empire, but over time it was granted various freedoms, beginning with maritime law, before establishing itself as a free city. The legal basis of the commune was established by Imperial decree, in the early 12th century.

There's a relative dearth of good primary sources concerning the History of Pisa, compared to say, the profusion of primary sources written in Florence about basically everything. Pisa was described as having a consular government, formed by election from candidates chosen from the leading patrician families.

In Italian communes, the Patrician families were not the aristocracy, with all the attendant Feudalism and serfs, but instead leading merchants, landlords and (as the period progressed, bankers). This was mainly because Cities tended to lack the landowning classes, and also lack a large amount of Fields. As such, there's less of a peasant class, and more of an urban working class. The food would be imported, brought to market, or traded for.

I'm afraid I don't know much more about the specific political system of Pisa, I studied Florentine history extensively, but barely touched on Pisan history. That said, Florence like most of the Italian communes operated a similar political system, although elections were held, its dangerous to describe them as being "democratic", voting participation was limited, the choice of candidates were limited, and the various systems were often open to extensive manipulation. That said, they're arguably more egalitarian than the Feudal, autocratic systems that were prevalent in the majority of Christendom.

Sources: A history of Pisa, 12th and Eleventh Centuries, William Heywood The Civic World of Early Renaissance Florence, Gene A. Brucker