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HAMBURG, Germany -- The long effort to legalize recreational marijuana in New Jersey could be delayed by an unrelated development that has dominated state politics for the past week.

State lawmakers and Gov. Phil Murphy want to pass a bill to legalize weed as soon as possible -- maybe as soon as the end of the month. One target date has been a vote on Oct. 29.

But Murphy's administration is now the subject of an investigation by the state Legislature over how his team handled a sexual assault allegation against a former senior staffer.

The Democratic governor said Wednesday he's optimistic the inquiry won't derail the progress of legalizing marijuana for adult use.

"I would hope that we can multitask," Murphy told reporters in Hamburg during a stop on a nine-day overseas business mission.

None of the state's top lawmakers -- all of whom are also Democrats -- have said publicly that the vote will be delayed.

But privately, lawmakers believe it's possible the work required to launch the investigation could push back the marijuana bill's progress.

State Senate President Stephen Sweeney, D-Gloucester, and a spokeswoman for state Assembly Speaker Craig Coughlin, D-Middlesex, declined comment Wednesday.

While Murphy is away, both houses of the Democrat-controlled Legislature announced Tuesday it plans to look into how his team handled allegations that a senior staffer who has since resigned raped a woman while working on the Democrat's campaign last year.

Katie Brennan, chief of staff of the New Jersey Housing and Mortgage Finance Agency, on Sunday publicly accused Albert J. Alvarez of sexually assaulting her while he worked on Murphy's campaign in April of 2017. Alvarez was never charged with a crime.

Brennan claims she alerted Murphy's team of the accusations three times over the last year. Alvarez remained in his job as chief of staff at the New Jersey Schools Development Authority until Oct. 2, when a reporter asked him for comment on the allegations.

Murphy has launched a separate independent investigation into Alvarez's hiring, headed by Peter Verniero, a former state Supreme Court justice and state attorney general.

NJ Advance Media staff writer Brent Johnson contributed to this report.

Matt Arco may be reached at marco@njadvancemedia.com. Follow him on Twitter @MatthewArco or Facebook.