Central Bureau of Investigation (CBI) sources said Tyagi and his brothers Julie and Docsa were questioned at the probe agency's headquarters.
"The Tyagi brothers were questioned for around eight hours," a CBI source said.
The CBI had Tuesday questioned Aeromatrix CEO Praveen Bakshi, former union minister Santosh Bagrodia and lawyer Gautam Khaitan in the case.
A CBI and defence ministry team had gone to Italy last month to collect documents concerning alleged kickbacks to clinch the deal.
The investigative agency filed a preliminary inquiry against 11 people on February 25.
Besides S P Tyagi, the inquiry names his cousins Sanjeev alias Julie Tyagi, Docsa Tyagi, Sandeep Tyagi, Khaitan (who was formerly associated with Aeromatrix) and Bakshi.
Others named in the inquiry include Giuseppe Orsi, former CEO of Italian defence major Finmeccanica; Bruno Spagnolini, CEO of AgustaWestland, a Britain-based subsidiary of Finmeccanica; and alleged middlemen Guido Ralph Haschke, Karlo Valentino, Ferdinando Gerosa, and Christian Michel.
The firms named are Finmeccanica, AgustaWestland, IDS Infotech Ltd (India) and Aeromatrix India.