As an Imperial citizen, your case would be processed under the Codex Justinianus, the laws laid down by the amusingly-named legal scholar Tribonian in the 7th century that formed the basis of Imperial law right through to the 15th Century.

Unless you were a soldier, you wouldn't be held in prison, but you could still be arrested and held by officials until your trial could be convened, preferably as soon as possible. Book 9, Title 3 states:

No accused person shall, under any circumstances, be confined in prison before he has been convicted. If he should happen to be a long distance away, the accusation shall not be received before the accuser formally agrees that, if he should fail to legally prove the charge, he will submit to the penalty which the other party would have suffered if he had been found guilty. A sufficient time, consisting of not less than thirty days, shall be granted by the judge of the district to the accused, for the purpose of arranging his business; and no more shall be granted to him who has been ordered to produce the defendant. After he has appeared in court, and an advocate has been appointed to defend him, the case shall be heard, and, whether the guilt or the innocence of the accused is established, he and his prosecutor must be treated in the same manner, without any distinction.

Title 4 states that trials should be brought as soon as possible, and also sets several guidelines for the treatment of prisoners who have not yet been found guilty, particularly to prevent innocent parties being tortured or murdered while in custody.

As soon as the defendant is produced in any case, whether an accuser is responsible for his appearance, or whether a public official has caused his arrest, his trial must at once proceed, so that if he is guilty, he may be punished, and if he is innocent, he may be discharged. When the accuser is absent, or the presence of the accomplices of the accused is considered necessary, they should be found as soon as possible. In the meantime, however, handcuffs should not be placed on the defendant, which bind him closely, but he should be placed in longer chains (if the nature of the offence demands the harshness of chains); so that he may not be subjected to suffering, but still remain in safe custody. He should not, however, be confined in a dark dungeon, but where he can be reached by light, and enjoy it; and, as night demands double vigilance, he ought to be lodged in the vestibule of a prison, or some other healthy place, and, when day returns, he should immediately be brought out into the light, as soon as the sun rises, in order that he may not die through imprisonment, which is considered unfortunate in the case of innocent persons, but not sufficiently severe so far as those who are guilty are concerned. The following rule must also be observed, namely, that it shall not be lawful for those who perform the duties of jailers, or their attendants, to sell their cruelty to accusers, by destroying innocent persons through confinement in narrow dungeons, or, by delaying the hearing of their cases, cause them to waste away with disease; for a judge is not only liable to loss of reputation, but he will also incur serious risk if he does not punish with the penalty of death any jailer or his attendants, who, through negligence, or for any other reason whatever, permit anyone to remain in prison a longer time than he should, or to punish by starvation.

For the theft of livestock, you would be liable for value of the same. Book 2, Title 9 states:

It is a well-established rule of law that a sheep thief shall bear the loss of stolen property, if this occurs before his offer to make restitution.

Murder, on the other hand, would be far worse for you. Book 9, Title 12 declares:

As many crimes are classed under the term "violence," and as force is often employed against those who resist, and blows are inflicted upon others who indignantly return them, and murder not infrequently results, it has been decided that if anyone, either on the side of the person in possession, or on that of him who rashly attempts to obtain it, should be killed, he must be punished who attempted to employ force, and was responsible for the injuries of either party, and he shall not merely be sentenced to relegation, or deportation to an island, but shall suffer death, and the judgment pronounced against him shall not be suspended by appeal.

Other punishments in the Byzantine legal system included prison, exile to penal islands, and forced labour, particularly in mines.