What are the laws in Sigil?

We have a glimpse of some of them on the Factol's Manifesto, page 110, plus the sentencing "reforms" instituted by Factol Nilesia associated with them:

The Mercykillers have posted declarations all over the Cage announcing their sentencing reforms, which they claim have "simplified" the process of punishment. Henceforth, all crimes committed in Sigil fall into one of three categories, and all crimes committed in the past get reclassified according to the new structure. For all felonies (such as murder, rape, burglary, or arson), the Mercykillers' new punishment is death. For all misdemeanors (such as assault, embezzling, jaywalking, begging, or vagrancy), the new punishment is 10 years' hard labor in the Lower Planes. And for all other rules infractions (such as failure to pay fines, falsifying reports, and so on), the new punishment is 10 years' incarceration in the Prison.

Factol Nilesia's said to have some sense of fairness, though. For instance, a berk who's already served more than 10 years for operating a tavern without a license is now free to go. But sods serving life for previously sentenced felonies are getting the hangman's noose.

The severity of this is moderated somewhat by the actions of Arwyl Swan's Son, another high-up in the Mercykillers, as described on page 107:

Often it seems to [Swan's Son] that the Red Death stretches the bounds of goodness in the name of justice - and even commits acts of out and out evil. So he tries to ensure that not a single sod goes to the gallows for a crime he didn't commit.

In the Cage, page 60, gives a little more context on the legal process, both in terms of passing law and some of the nature of it.

The Clerk's Ward takes pride in its progressive policies regarding capital punishment (in most cases, an execution's got to be preceded by a fair trial) and free enterprise (merchants may engage in trade without government interference - within reason). While these are strictly speaking a function of the Court in The Lady's Ward, the Clerk's Ward prides itself on having been instrumental in their implementation.

Other proposals, currently under discussion at the Hall of Speakers, include:

• The Architectural Uniformity Act, establishing official color schemes for all structures in the ward.
• The Indigent Relocation Act, collecting funds to purchase wagons for moving impoverished citizens to the Hive Ward, where it's felt they'll be more comfortable.
• The Apparel Regulation Act, establishing dress standards for workers and making violations punishable offenses.

None of these proposals've become law. But debate'll continue, perhaps for years, perhaps for decades. A thorough discussion's always preferable to a hasty decision.

ZwiQ mentioned the execution process, though that's the process as of Hashkar 126 (when ItC is internally set), when Factol Mallin still ran the Mercykillers. This information was supplanted by new procedure in Hashkar 127 (when FM is internally set) after Factol Nilesia took over, which is also why the categorization of crimes is slightly different there; while desertion and escaping slavery aren't mentioned in FM's categorization, I would imagine they are still crimes even after she took over, as she wouldn't have the authority to legalize activity on her own. There's also a new execution process under Nilesia's direction, as described on page 105 of the Factol's Manifesto:

The Mercykillers have always carted off "special" prisoners to Petitioner's Square, a public place where jeering crowds can watch a berk get hung, beheaded, or eaten....But most of the inmates met their deaths in the deepest, quietest corner of the Cellars. By the time sods learned where the execution chamber was, they were already standing in line.

Now, though, Factol Nilesia's mandated that the inmates be put to death in the open square inside the Prison's four walls. During her first month in office, she had a tremendous gallows built in one corner of the square, directly above a heavily guarded pit said to lead to the Cellars. Deaders get dragged underground and sent through portals to a special area in the Mortuary that handles executed prisoners.

The daily hangings are mandatory viewing for prisoners. Each day, inmates from one floor of the Prison file out to the square. Under heavy guard, they're forced to witness the hangings of fellow inmates whose crimes fall under the death punishment in the new sentencing procedures. Nilesia feels the example will help them avoid making similar mistakes in the future.

A good resource is TSR 2609, In the Cage: A Guide to Sigil. On page 21, there is a subsection titled "Writing the Dead-Book: Executions in Sigil".

... hanging is reserved for deserters, embezzlers, murderers, and escaped slaves.

Execution by the blade is generally reserved for nobles and powerful faction members - high-ups guilty of crimes such as seeking to close a portal to the Outlands, failing to provide taxes to the city treasury, libeling the Lady, or such like.

Death by the Wyrm is an extremely rare, lingering, spectacular demise. ... only traitors to the city (those who betray the trust placed in them, such as those who slay dabus, those who reveal secret gates, or those who charge tolls and tariffs on the Lady's portals) are sentenced to death by the Wyrm ...

For a Sigil-specific crime, ItC:AGtoS gives an example on page 54, discussing the dead deity of portals, Aoskar:

His followers are very few and very peery, for they are hunted ruthlessly and often sentenced to a gruesome death by the Wyrm for their beliefs.

On the other hand, TSR 2624, Uncaged, Faces of Sigil, has details about Will of the One, a group who wants to resurrect Aoskar, and on page 37, while describing Fell, a dabus proxy, we read:

A growing number of Signers suspect that Fell is a proxy of the portal-god immune to the Lady's wrath, though to hold this view publicly is to invite a beating from the Harmonium and the Mercykillers.