For smaller cities, one definitely needs access to specialist literature in italian, so this will be more of a general developmental and institutional trend, which definitely differs across the cities, and likewise, some autonomous cities (or city-states) did not necessarily have any different institutional make up than other non-autonomous cities, other than having a representative or other person from outside governing source, but amount of such influence, again, varied.

Depending on how one understands "constitutional", well, might be somewhat problematic, as although cities usually had statutes, their administrative/governing bodies were anything but constant, varying both in numbers, powers, requirements, etc. I can probably go into some specifics for northern adriatic coastal cities, but most of them would later fall under venetian control.

The commong characteristic was definitely gradual decline of arengo (general assembly), which functions were overtaken by different councils (consiliums) and other collegiate bodies, with executive consulates. With development, the latter function in some cities also differentiates between execitve and judicial consuls. For example, Pisan consuls (mid twelfth century) were accounted to the council (which was made of permanent familial senators and 24 elected from the general assembly from each of the city quarters). These great councils varied in numbers significantly, from less than a hundred to more than five hundred, depending on time and place. Smaller councils were typically only the inner circle working with the consuls and later podestas, to which I will return. Another institution worth mentiong here would be commissions (balia and savi) that were appointed in times of need and specific issues that required flexibility, expertise and responsiveness.

By the second half twelfth century, we also see the rise of Podesta (under Habsburgs, Hauptmann or capetaneus), which became the principal executive and judiciary person, sometimes a delegated foreigner with a rather short mandate, or local nobility. In cases of autonomous cities, it was elected by a collegiate body, in non-autonoumous cities, it could be appointed.

Some other commonalities were financial offices, usually run by a camerarius, notaries and other persons for things such as enforecement, revisions, audits, archives, ... It goes without saying that when these changes happened, and other specifics within these general bodies (procedures, statutes, compositions, electoral process, naturally ecclesiastical interactions, etc ) differed.

The only introductory english book on administration of northern Italian cities that comes to mind, although I have not read it, is,

Waley and Dean, (2017). The Italian City-Republics. 4th ed. Routledge.