Your Cyrodilic bounty does not apply in the Isles, nor does any bounty from Lord Sheogorath's realm apply in Cyrodiil.
If you commit a crime in front of a guard, or in front of a citizen who reports your crime, a bounty will be placed on your head (as in Cyrodiil) according to the seriousness of your crime. Any Golden Saints or Dark Seducers in the area will attempt to arrest you. Talking to any such guard with a bounty on your head will result in an arrest. If your bounty is over 1000 gold, any guard you see will attempt to arrest you. Arrest results in the same options as in Cyrodiil, with two exceptions.
Opting to go to jail in the Shivering Isles has the same connotations as outside them, but jailbreak is treated differently. If you are arrested by the Saints of Mania, you will be thrown into a cell at Aichan. If the Seducers of Dementia arrest you, you will be imprisoned in Corpserot Passage. In both cases, you will find a switch in your cell. Pushing the switch will cause one of the walls to retract, allowing you to attempt a jailbreak. There is no bounty for this, but you will have to fight your way out of the dungeon, including fighting a Golden Saint/Dark Seducer Turnkey at the end. Should you win, your possessions are in an Evidence Chest at the end of the dungeon and you are free to leave, your bounty cleared.
 Go with Guard
Becoming Madgod of the Shivering Isles has certain benefits. While your crimes will not go unnoticed, the resident guards are more likely to be lenient with their Lord Sheogorath. An additional option will replace that of "Go to Jail"; you may journey with the guard to New Sheoth Graveyard in Dementia, or a small unmarked structure north of Bliss in Mania. There your stolen goods will be confiscated and taken to Aichan or Corpserot Passage, but you are welcome to continue your life without paying the fine, until such time as you can acquire necessary funds. You will, however, still have a bounty on your head. Resisting arrest is mostly the same, except that the daedra will be utterly thrilled to be slaughtered by you.
 Pay Gold
If you opt to pay the fine, as with the "Go with Guard" option, your stolen goods will be confiscated and will be waiting for you in the Evidence Chest in either Aichan or Corpserot Passage.
If you attempt to attack Lord Sheogorath, you will be teleported above Execution Point to fall to your death.
 The Fringe
The Fringe does not possess a jail, so it is not possible to go to jail or pay off your bounty there. If arrested in the Fringe, the only choice is to Resist Arrest. This is due to the fact that without a jail, the normal commands used to send the player to jail are non-functioning.
- Any bounty acquired after becoming Madgod cannot be paid off. More information can be found here.