It is alleged Giuseppe Profiti and Massimo Spina, respectively the former president and treasurer of the Bambino Gesu hospital, used the hospital money to renovate the apartment of a top cardinal.
If convicted under Vatican legislation concerning conspiracy to commit a crime and misappropriation of funds, the pair each risk being jailed for between three and five years.
The funds were used to improve the flat of Cardinal Tarcisio Bertone, an 82 year old who was effectively deputy pope prior to his retirement.
According to Reuters, the court did not reach a decision on Tuesday over whether Bertone - who isn't accused of any wrong-doing - should be called to give evidence in the case.
The news agency also reported that the two men's lawyers unsuccessfully argued that journalists should be barred from future hearings and be restricted to watching proceeding via video link.
They also wrongly claimed the hospital is in Italy - and therefore outside the jurisdiction of the Vatican court. But the site was donated to the Holy See in 1924.
Speaking previously, Mr Profiti claimed the hospital funds spent on Bertone's apartment were in return for the cardinal agreeing the property could be used for fundraising efforts.