WASHINGTON — The House Oversight Committee said Monday it is investigating whether Transportation Secretary Elaine Chao acted improperly to benefit herself or her family’s shipping company. Two Democratic leaders sent Chao a letter asking her to turn over documents and communications related to the New York-based company, Foremost Group. Chao’s father and sisters own the company, which transports material to and from China. “Federal regulations prohibit federal employees from using their public offices for ‘the private gain of friends, relatives or persons with whom the employee is affiliated in a non-governmental capacity,’ ” the lawmakers wrote in a seven-page letter to Chao. The New York Times and Politico have reported that Chao may have used her Cabinet position to benefit the company and increase its influence and status with the Chinese government.