NEW YORK (CNN/Money) - Tyco International Monday sued a former board member, Frank Walsh, demanding he return $20 million paid for helping the troubled conglomerate buy CIT financial services unit last year.

Tyco said Walsh, a director until February, kept mum about the fee from L. Dennis Kozlowski, Tyco's former chairman and chief executive, who was indicted earlier this month on charges of evading more than $1 million in sales tax.

Tyco wants return of the money, half of which went to a charity, and has sued for damages, according to a filing in federal court in Manhattan.

Responding, Walsh, who acknowledged the $20 million payment, called the lawsuit an overreaction to the "recent and well-reported problems and management changes at Tyco. "

Walsh said in a statement that his more than 30 years of deal-making experience allowed him to seal the CIT purchase for Tyco, giving the conglomerate access to an important business it now must sell.

A selloff in Tyco shares accelerated in January when the company announced the payments -- a $10 million fee to Walsh for helping and another $10 million his charity, the Community Foundation of New Jersey.

But Tyco Monday called the payments "unauthorized" and said Walsh has refused to return the $20 million.

"Walsh ultimately induced Kozlowski to agree to pay him," said the lawsuit, which alleges that the board was never notified as it should have been of payments made in last July. "Walsh breached his fiduciary duties to Tyco and induced Kozlowski to breach his duties to the board."

Shares of Tyco have been on the rise since the Securities and Exchange Commission late last week cleared the way for the company to sell its CIT unit in an initial public offering. But Tyco shares are still down about 75 percent year-to-date as investors fret that the company, hit by a series of scandals, overstated profits.

Walsh did not address to charges, beyond calling the suit an overreaction. For its part, Tyco, by demanding $20 million, implied that the New Jersey charity should give up the $10 million.

The Walsh suit was just one that Tyco filed Monday. The company also accused former general counsel Mark Belnick of engineering a cover-up that included destroying documents and not disclosing the criminal subpoena of Kozlowski.

The alleged cover-up by Belnick, Tyco said in a statement, included concealing $35 million in pay he collected for himself that was not approved by the board.

Both suits come since Tyco hired a new general counsel of Boies, Schiller & Flexner -- a firm whose past clients have included Al Gore and Microsoft.