Venice was founded by refugees fleeing Aquileia from the Lombard invasion in about 568.

By 584, those parts of the east Italian coast still in the hands of the Byzantines, rather than the Lombards, were organized into the Exarchate of Ravenna by the Eastern Roman Empire. The islanders (who were developing into Venice) were included in this.

150 years later, in 726, the Venetians for the first time elected their own Doge (Duke), specifically as an opponent (or local champion alternative) to Byzantine rule. This bid for independence (if such it really was) failed, and Byzantium continued to rule Venice.

In 751, the Exarchate of Ravenna fell. Now the Venetians, though still legally part of the Eastern Roman Empire were becoming more and more de facto independent.

In 809, the Venetians allied themselves to Pepin (son of Charlemagne) without reference to Constantinople regarding the allegiance.

In 814, The Franks and the Byzantines made a treaty which established that Venice would not be a part of the Holy Roman Empire. It did not mention the relationship between Venice and Constantinople (but perhaps implied that Venice was still part of the Eastern Roman Empire).

In the late 11th century, the Venetians aided the Byzantines against the Normans (who were conquering Byzantine possessions in Southern Italy). The Byzantines, confirmed at this time that Venetians could trade freely throughout the Byzantine Empire without paying any dues or customs.

This was an interesting moment. It seems to have confirmed that Venice was de facto independent (why confirm the normal freedom of trade for a part of your empire), but also to still imply that Venice was officially still part of the empire (of course you can trade freely, you are part of us).

The Venetian constitution evolved between 1140 and 1160, with various councils taking more and more power from the Doge, and Venice becoming an oligarchic republic. Certainly, by now (probably long before), Venice was de facto independent of the Byzantine Empire.

There does not seem to be any point where Venice became "officially" not a part of the Byzantine Empire, though by 1203, when the Venetians conspired to divert the 4th Crusade to attack Constantinople it seemed that they were definitely not part of the Empire.

Or were they? The Venetians would have claimed that they were operating in support of the unjustly deposed Emperor, Alexius.

Although the Crusaders initially took Constantinople in the name of Alexius, when he could not pay Venice what he had promised, the Venetians persuaded the Crusaders to sack Constantinople, and they seized various Byzantine territories.

It was from this event that all remaining tenuous claims (on both sides) that Venice was a part of the Byzantine Empire were pretty much dropped (by both parties), though I don't believe there was ever an "Official Moment" marking the independence of Venice.

In summary, de facto, Venice became independent from Byzantium in a gradual process which probably was mostly complete around 751. Official Independence was never formally announced, but was universally aknowledged, with not even any tenuous fictions remaining after 1204.

http://www.historyworld.net/wrldhis/PlainTextHistories.asp?groupid=432&HistoryID=aa43&gtrack=pthc