No, Venice actually purposely rejected Roman/Byzantine law and used their own customs and traditions:

“Venetian law was a system based on upon written statutes, a body of case law cobbled together out of previous decisions, and custom, rather than a rational and ordered system of Roman law drawn up by skilled jurists. This attitude can be traced back to Venice’s historical claim to be independent from the authority of the empire, but it also suited an amateur judiciary very well. Venetian legal documents are in fact remarkable for their lack of reference to jurisprudence or learned opinions.” (Shaw, pg 13)

This was certainly the case in the 10th century. Venice was a relative small and compact oligarchy controlled by a few noble families, and the judicial aspects of the Doge’s powers were inseparable from his political power. The legal courts were simply the Doge’s court, and the people in charge of making legal judgements were the other nobles, who were proud of their amateur status. Their neighbours in northern Italy used Roman law, or the Germanic (but Roman-influenced) Lombard law. Territories in Italy and the Balkans controlled by the Byzantine Empire used Byzantine law, which was ultimately based on Justinian’s codex and ancient Roman law, but the Empire’s laws had also evolved since Justinian and they had other legal codes by the 10th century as well. But not Venice, they had no organized code of law at that point.

By the 12th century, Venice was much bigger and more powerful and it was becoming impossible to govern legal disputes using only this old, confusing body of precedents and customs. The Doge’s court could no longer handle all the property disputes and criminal cases that arose in population of a hundred thousand citizens or more. In 1195, Doge Enrico Dandolo (who is otherwise most famous as a leader of the Fourth Crusade that conquered the Byzantine Empire) created a rudimentary written legal code. This was revised several times throughout the 13th century, by his son Ranieri Dandolo, and by Doges Pietro Ziani and Giacomo (or Jacopo) Tiepolo. Tiepolo’s law code from 1242 was the basis for all Venetian law thereafter. It was also used in Venice’s other territories on the mainland of Italy and along the Adriatic coast, and in their colonies further away in Crete and Cyprus.

There would have been one outside law used in 10th century Venice though - the “Lex Rhodia” or the “Rhodian Sea Law”. That was a very ancient custom governing the risks and responsibilities of sea travel, trade, shipwrecks, etc. It was at least as old as the Roman Empire and may have dated back even further to the Greeks or even the Phoenicians. There was a sort of standard edition written on Byzantine Rhodes in the 9th or 10th century, and all the Mediterranean sea-faring cities and states tended to adopt it. Otherwise, Venice didn’t use Roman/Byzantine law or the customary Germanic law of Lombardy. They just used their own confusing mass of traditions and the only court was the Doge’s political court.

Sources:

Frederic C. Lane, Venice: A Maritime Republic (Johns Hopkins University Press, 1973)

Donald E. Queller, The Venetian Patriciate: Reality Versus Myth (University of Illinois Press, 1986)

Thomas Madden, Enrico Dandolo and the Rise of Venice (Johns Hopkins University Press, 2003)

James E. Shaw, The Justice of Venice: Authorities and Liberties in the Urban Economy, 1500-1700 (Oxford University Press, 2006)

Thomas Madden, Venice: A New History (Penguin, 2012)

There’s also an edition of the Statues of Giacomo/Jacopo Tiepolo, although it’s in Latin and Italian:

Gli Statuti veneziani di Jacopo Tiepolo, ed. Roberto Cessi (Venice, 1938)