One focal point has been Adam Skelos’s hiring by an Arizona company, AbTech Industries, as well as a storm-water treatment contract that AbTech was awarded by Nassau County — the senator’s political backyard — even though the company was not the low bidder. Another area of inquiry has been a $20,000 payment to Adam Skelos from a title insurance company that he never worked for.

According to people familiar with the questions being asked by federal authorities, investigators are seeking to determine whether Senator Skelos exerted any influence in matters involving AbTech. They are also examining whether his son’s hiring as a consultant was part of a scheme in which the senator, in exchange, would take official action that would benefit AbTech or another company, Glenwood Management, a politically influential real estate developer that has had ties to AbTech.

Any such action could pose a conflict of interest or potentially violate federal corruption statutes. It is unclear what actions, if any, Senator Skelos has taken in connection to his son’s business dealings, or how they relate to state government; neither man has been accused of wrongdoing.

All of the people who spoke about the investigation did so on the condition of anonymity because of the delicate nature of the subject.

The investigation is being conducted by the office of Preet Bharara, the United States attorney for the Southern District of New York, who has embarked on an assault against graft and other political misdeeds in Albany, describing the capital as a “caldron of corruption.” His critics have accused him of grandstanding, and say his unusually blunt public condemnations of how business is done in Albany have crossed the line for a federal prosecutor.