There's no doubt Caroline Kennedy is wealthy. As part of one of America's most famous and well-off families, she counts ties to exclusive properties and institutions that date back generations.

With a bid for public office, many of those sensitive links normally become public, as they have for others vying for Hillary Clinton's seat.

But not for Kennedy. She's refusing to divulge her financial interests unless picked for the post, another quirk of an election-free Senate race that's perfectly legal, but troubling to some.

"Technically she's not a candidate in the true sense of the word. But that doesn't mean that she shouldn't come forward with the kind of disclosure that would be required of other candidates," said Dick Dadey, Citizens Union.

Ultimately, Governor Paterson will have the final decision.

"If Governor Paterson were to choose Caroline, she would, of course, comply with all disclosure requirements," said a Kennedy spokesman.

That would include a form outlining investments and other income for a candidate and his or her spouse.

It's unclear what Paterson himself is asking candidates. A spokesman said they will be vetted the same way Paterson's cabinet picks were, which involves a police background check.

Individual candidates, however, decide whether they want to make anything public.

"It's precisely because there is no campaign or election that she should release information, so that the public gets to know who she is and what she stands for," said Dadey.

Meanwhile, growing concern about Kennedy's campaign is prompting one of her supporters to tell Paterson to hurry up.

"The governor should make a decision reasonably quickly because this is just getting out of control," said Mayor Michael Bloomberg.

Some in the state's congressional delegation are questioning Kennedy's credentials, although others think her connections and service will boost New York.

As for picking someone quickly, the governor's spokesman responded by saying Paterson will move fast, once Clinton is officially confirmed as secretary of state.