The request is the latest escalation in the feud between Attorney General Andy Beshear and Gov. Matt Bevin.
Bevin took office in December and replaced Beshear's father, two-term Democratic Gov. Steve Beshear.
Beshear's letter to the commission requesting an investigation came days after Bevin announced he would hire a private law firm to investigate whether the former governor violated procurement laws and coerced state workers to donate to campaigns.
Bevin spokeswoman Jessica Ditto said the administration would welcome a parallel investigation. She did not respond directly to Andy Beshear's allegations.
Andy Beshear said the ethics commission should investigate allegations about political donations.