FRANKFURT (Reuters) - Germany's financial markets watchdog is investigating whether Deutsche Boerse should have provided more information to investors during its search for a new chief executive, with a ruling against the company potentially leading to a fine.

A spokeswoman for the BaFin watchdog said it was looking into whether the German stock exchange operator should have publicly disclosed that a personnel committee on the supervisory board had on Nov. 13 narrowed its CEO search to two candidates.

On Nov. 16, Deutsche Boerse announced that Theodor Weimer would be its new chief executive officer.

German law requires companies listed on an exchange to publish information that could affect share prices in a timely fashion. The rules are in place to prevent insider trading.

Failure to do so can in theory cost up to two percent of a company's annual revenue, or 48 million euros ($59 million) in this case.

A spokesman for Deutsche Boerse said the company took its duties to promptly inform the public very seriously. "These duties were also carefully considered in the selection and appointment of a new chief executive officer," he said.

Instead of waiting three days to announce the final decision, Deutsche Boerse could have been required to announce that it had short-listed two individuals, without naming names, said a person familiar with the matter.

That could have cleared up concerns about a leadership vacuum, said the person, who was speaking on condition of anonymity due to the ongoing investigation.

Separately, BaFin has dropped an inquiry into a July 18 announcement by Deutsche Boerse about the status of an investigation into its previous CEO, the BaFin spokeswoman said.

WirtschaftsWoche first reported the news on BaFin's investigations.

($1 = 0.8145 euros)

(Reporting by Andreas Framke; Writing by Tom Sims; Editing by Mark Potter)