The Maryland Court of Appeals gave former Prince George's state senator Tommie Broadwater Jr. a second chance yesterday to challenge a 1984 state constitutional amendment that prohibits anyone not registered to vote from holding elective office. Broadwater was convicted of food stamp fraud in 1983 and cannot register to vote until his parole is over in 1988.

Eager to regain his Senate seat, he challenged the legality of the amendment last October in Anne Arundel County Circuit Court, but the judge dismissed his suit. The appeals court ruled yesterday that Circuit Judge Bruce C. Williams should not have dismissed the case without proper discussion of the issues involved, and ordered the case returned to Circuit Court.

Broadwater has argued that the constitutional amendment proposed by the General Assembly and approved by the state's voters was aimed solely at keeping him out of office and is, therefore, illegal. He has repeatedly stated that he wants to regain the state Senate seat that he lost when he started serving a six-month term in a federal prison.

As a convicted felon still on parole, Broadwater, a Democrat, could not run as the endorsed candidate of a political party. The constitutional amendment sought to close a loophole in the law that would have allowed Broadwater to run in 1986 as an independent.

Eric S. Slatkin, an attorney for Broadwater, said the state appeals court decision is "better than losing" but that he had wanted the court to decide the merits of the case. If the case is heard and lost in circuit court, then appealed, he said, the 1986 elections may be over. "We don't have much time," he said.