A poll released by Democrat Steny Hoyer yesterday shows Hoyer with a 15-point margin over Republican Audrey Scott in the Prince George's County race for Congress. The results, released yesterday, indicate that Scott will have a tough fight in the May 19 special election, despite infusions of cash and other campaign support from the national Republican leadership.

The poll and a second issues survey released yesterday also revealed continued high support for President Reagan and general support for his economic program among voters in Maryland's 5th District, which includes the nothern half of Prince George's and Takoma Park in neighboring Montgomery County.

Nonetheless, the voters in the heavily Democratic suburban district said they did not favor many specific Reagan-proposed cuts and believe a Democrat will most effectively represent them in Congress, according to the two polls.

The first poll was conducted by Potomac Survey Research, a local polling firm specializing in Maryland races. Its results parallel those found by the Scott campaign in their own recently released survey. But while the Scott poll showed Hoyer ahead, it was with a much narrower six-point margin that many Democratic and Republican observers found surprising given the country's 3-to-1 Democratic registration.

Hoyer's poll, which involved telephone interviews with 521 registered voters, showed that 53 percent of those surveyed supported Hoyer and 38 percent favored Scott. The remainder said they had not yet decided who to vote for on May 19. Scott's poll showed Hoyer ahead with 47 percent, 41 percent for Scott and 12 percent undecided.

The second survey also released by the Hoyer camp yesterday was conducted by the Democratic National Committee a week ago and elicited opinions on a variety of national issues from some 350 registered voters.

Hoyer Campaign Manager John McDonough said that the poll results confirmed what he felt was an increasing lead for Hoyer in the race to fill out the term of former congresswoman Gladys Spellman, who suffered heart failure last October. "It showed us a little further ahead than we anticipated, but it's been confirmed by our phone bank [which since the April 7 primary has called over 10,000 Democratic voters]," he said.

Scott campaign spokesman Jim McAvoy questioned the accuracy of the Hoyer poll, noting that it was conducted over two weeks ago and that its voter sample was based on registration figures instead of actual voting records, which McAvoy said would not so heavily favor the Democrats.

"Two and a half weeks is an awfully long time in a political race," McAvoy said. "If we both polled right now I think the results would be quite different from either his poll or ours. I don't know which way, to be quite frank."

In addition to the 15-point margin, the poll showed that despite a fractious 19-person primary, 67 percent of the Democrats polled support Hoyer. His strongest support was among moderate and liberal members of his party.

Scott came out of her crowded primary with even larger support among her party, according to the poll. However, nearly a third of the Republicans who voted for Scott's major primary adversary Lawrence Hogan Jr., said they will vote for Hoyer May 19, in part because of the harsh campaign tactics employed by Scott against Hogan in the primary.

The poll also found that of the women surveyed in the Hoyer poll, 54 percent said they will vote for Hoyer, 36 percent for Scott and 10 percent said they were undecided. That figure was a surprise to Hoyer campaign officials, who said they had assumed that Scott, as a woman in public office, would do better than Hoyer among women voters.

When broken down by legislative district, the poll results show Hoyer beating Scott in every area of the country except Bowie, Scott's home town where she has served as mayor for six years.

The poll also showed that few voters cared that Hoyer lives outside the 5th District -- by four blocks -- or that he has long been associated with the powerful local Democratic orgainization that critics call a political machine. Scott has hoped that both issues would prove to be of serious concern to voters and she has raised them frequently at political gatherings.

On national issues, the Hoyer and DNC polls both show support for Reagan, although a majority of those polled said they opposed most of the cuts he has proposed in social programs. And while those polled expressed general support for some form of tax cut, more than half of them felt the three-year Kemp-Roth proposal put forward by Reagan would most help the rich and would fuel inflation.

And when asked, "Who do you think can best help your congressional district -- a Democratic representative working with a Democratic controlled House of Representatives or a Republican representative working with a Republican president?" 56 percent answered Democrat and 35 percent said Republican. Another 19 percent said there would be no difference or they did not know.