As part of a new campaign to end tax evasion, the Greek government has accused shipping heiress Christina Onassis with failing to submit a tax statement on the inheritance of her father's Greek-based assets and has indicated that she may owe about $45 million in back taxes.

Stelios Papadimitriou, Onassis' legal representative in Athens, was not available for comment on the charges, which were made in a Finance Ministry announcement yesterday. Onassis is reported to be contesting the state's demands on the ground that assets inherited from her father, shipping tycoon Aristotle Onassis, after his death in 1975 were in the form of companies based in Greece but owned by Panamanian-based concerns.

The case against Christina Onassis is the most spectacular since the Finance Ministry launched a drive in January to curb widespread tax evasion. The practice is believed to be so widespread that it cost the government about $2.5 billion in 1981--almost equal to the balance of payments deficit for that year.

Onassis' inheritance is known to include Olympic Airways, the national airline company sold to the state shortly after Aristotle Onassis' death, and the Piraeus-based Springfield Shipping Co.

The Finance Ministry announcement said an employe has been dispatched to Panama for an investigation. Finance Minister Emmanuel Drettakis also has ordered an investigation into the finances of Olympic Airways.

While the authorities hope that their publicity of the new campaign will prove a deterrent in the future, they have backed up their efforts to unveil tax deceit by opening telephone lines to the Finance Ministry for private citizens to report offenders.

The program has aroused wrathful criticism from opposition parties.