The mysterious case of Anthony L. Conrad, the former chairman of RCA Corp., continues.

New York Gov. Hugh L. Carey has signed a request to extradite Conrad from Maryland so he can stand trial here on charges of income-tax evasion.

Conrad was removed as chairman and president of RCA a year ago after the company's directors learned he had failed to file federal, state and local income tax returns from 1971 through 1975. However, the bulk of his tax obligations for those years was paid through automatic withholding.

Approximately $70,000 still was owed to New York State but has been paid by Conrad, according to Assistant State Attorney General Moses Weintraub. However, Conrad has failed to show up three times for arraignment here on tax-evasion charges and the state is pursuing extradition because "we can't ignore it," Weintraub said.

The former business executive has denied through attorneys that any fraud was involved but has never explained why he failed to file the returns. He has been living at his home in Gibson Island, Md., on the Chesapeake Bay.

Carey's request goes to Maryland Gov. Blair Lee. Under Maryland law, Conrad is entitled to an executive hearing if he wants to challenge ex-tradition, and he also can appeal an unfavorable ruling to the state courts. So an extradition proceeding could turn out to be very lengthy.