Tosca is set during a very specific series of events: the Papal administration, forced out of Rome by revolutionaries inspired by the events happening in France, had recently reclaimed the city and imprisoned the leaders of the Roman Republic. The protagonist Cesare Angelotti, after escaping from his prison in Castel St. Angelo, is now one of the most wanted fugitives in the country, his crime being having been a Consul of the now-extinguished Republic. Baron Scarpia, the primary villain, as chief of police would not only naturally make capturing the escaped prisoner his top priority, but the libretto also gives him a romantic motive to further explain his dogged pursuit; he's lusting after Tosca, the lover of Angelotti's accomplice, Mario Cavaradossi (if I recall correctly. It's been awhile since I've seen the Tosca).

Although I think Puccini gives Scarpia an additional motive for the sake of drama, not to make the manhunt more plausible, it's true that the Papal censorship could be very lopsided in its application. Generally, only those deemed to be leaders of the most "subversive" movements were at risk of imprisonment and/or execution, and oftentimes the risk of crackdown was only consistent or really tangible in the city of Rome.

In fact, after the post-Napoleonic restoration, the Napoleonic police apparatus was initially retained because it lent itself well to reactionist censure. However, very little was done to guarantee it remained efficient and it was allowed to disintegrate by the 1820s. In little over a decade, the the Papal leadership had reinstated old feudal and ecclesiastical rights that caused judicial applications to become harsher on paper, while in reality becoming increasingly inconsistent. This reactionism ended with the final dismantling the Napoleonic police and bureaucratic apparatus, and the result was administrative chaos and breakdown of law and order. By the 1830s some regions were in a state of endemic revolt.

However, other parts of the Papal States were surprisingly innovative and lenient. In the Romagna, a region encompassing southeastern third of the fertile and densely populated Po basin, saw local leaders create leading agricultural cooperatives that encouraged development. Law and order was generally maintained. But this is more attributable to the history of self-government in that region; the bourgeoisie in Bologna, the administrative center of the northern Papal States, had even lobbied the Congress of Vienna to be assigned to the Austrian Empire rather than return to the regressive Papacy.

If you're interested in going more in-depth, John A. Davis, literally opens his Italy in the Nineteenth Century with a nifty chapter titled “The Age of Restoration: Napoleon’s legacy and restoration administration.”