(CNN) Here's something you don't hear too often these days: Republicans might have a shot at flipping a House district in Connecticut.

Democratic Rep. Elizabeth Esty from Connecticut's 5th Congressional District is in hot water over how she handled abuse allegations made against one of her top aides in 2016.

After learning of allegations of threats and physical assault made against her chief of staff, Esty kept the top aide on for three months before entering into a nondisclosure agreement with him and writing him a recommendation letter, CNN reported Friday

Esty said she won't resign, and Republicans currently lack a top recruit to challenge her in November's election. But there's still two months before the filing deadline, and a source familiar with the National Republican Congressional Committee's recruiting efforts told CNN the committee is reaching out to potential challengers.

It won't be an easy battle for Republicans to win a seat given the national environment, but this is the type of district and scandal where Republicans could conceivably mount a strong challenge.