This claw of an island, three miles long and one mile wide, is attached to a crooked arm of the Eastern Shore by a single drawbridge. Home port of the oyster-dredging skipjacks, America's last commercial sailing boats, the Chesapeake Bay community looks quiet and picturesque.

But for years, islanders say, they have had to deal with their share of problems, mainly the minor offenses of rowdy young residents.

The youths have littered Kronsberg Park, with its memorials to drowned watermen, island doctors and veterans, island residents say. The young people have hurled insults and worse at the tourists coming over the busy Knapps Narrows drawbridge and at the Topsider set going under it.

They have also warred with the owner of the Bridge Restaurant, an outsider who turned a watermen's drinking hole into a more elegant and higher-priced establishment.

Whenever state police drove the 22 miles from Easton, the closest Maryland post, they found few islanders willing to talk, including the time someone poured sugar into the gas tanks of earth-movers being used to build a sewage treatment plant.

By and large, the 870 islanders suffered in silence or took matters into their own hands, state police said.

"Tilghman has always been that way," said Cpl. Thursby Cooper of the Easton state police barrack. "It's like any bay island. They're all kind of independent people. When we go down there to investigate crimes , nobody knows anybody."

Now, however, law and order -- or the lack of it -- is the open talk of Tilghman. And islanders are talking, to state police as well as to each other.

It all began just months after a visit by President Reagan had turned Tilghman into what the Easton Star-Democrat described as a "police state to accommodate the leader of the world's greatest democracy." In January, with life back to normal, the island's only bank was robbed.

"It was the first-ever bank robbery [here]," said postmaster Phyllis Sadler. "Everybody said it wouldn't happen because they could never get away."

But the two thieves escaped over the bridge, sending shudders down the spine of Rte. 33, all the way to Bar Neck and Black Walnut Point, at the southern tip of the island.

"That bank robbery terrorized the entire community," said Peggy Grogan, who with her husband Carl owns the Tilghman Country Store. "That night, everybody was watching everybody."

Two suspects in the bank robbery were eventually arrested. They were not from the island but from Hurlock and East New Market over in Dorchester County. One of them has pleaded guilty.

However, the bank holdup paled in the minds of many residents in comparison to an incident during the Tilghman Elementary School PTA talent show in Feburary. That's when Hank Cook, a Cambridge, Md., radio announcer who had volunteered to be master of ceremonies, had his car trashed.

Cook emerged from the event to find his station wagon's dome light broken and human excrement on the seats.

Islanders were upset and embarrassed. They apologized, agonized and organized. In the weeks since, they have held several meetings, packing the local firehouse twice. And they have formed, for the first time in island history, a neighborhood crime watch, complete with block captains.

Tilghman, to be sure, has changed over the years: The old bank is now Ye Olde Bank Shoppe, there's a new French-style restaurant, and Buddy Harrison's Chesapeake House hotel and restaurant is adding a wing. But a neighborhood crime watch at first blush seems out of place in this rural community.

Newcomers, mainly older couples who have chosen Tilghman for retirement, and natives have united in their determination to make the island safe for all. But they don't want to make a big stink about it.

Residents want to "keep it within the community and try to help the kids who did it," Sadler said. Who did it, however, is not clear. There have been no arrests in the PTA talent show incident and no public censor of the culprits. State police are investigating.

"That [incident] was a pretty bad deal," said Calvin Lewis, who works at Gary Fairbank's tackle shop and general store, where watermen gather early each morning. "It's just a few that make the island look like a bad place."

Because this is a small and somewhat isolated community, said Jane Page, who has lived here for 42 years, "everybody's related to one another and . . .people don't want to report [incidents]. But now, it's come to a head."

Said Francis (Smiley) Cole, sitting at the bar of his Bridge Restaurant, "This is a good, decent place to live. It just needed something to bring them together and set these rascals packing."

Cole wanted to offer a $1,000 reward for the capture of the culprits. The PTA show organizers offered Cook compensation and a car to drive home.

Cook wanted none of it.

"I didn't want to impose," he said. "To me, it was not that serious . . . . It could've happened in Philadelphia, Baltimore or Crapo [Md]. . I don't think it reflects the people there . . . .I would love to be invited back.