UPDATE 2-Cooper Industries seeks to relocate to Ireland

* Shareholders to vote on reincorporation

* Stock down 4.4 pct

* Citi estimates index funds hold 22 mln shares (Adds analyst comment, detail on NYSE listing, share reaction)

NEW YORK, June 9 (Reuters) - Cooper Industries Ltd (CBE.N) said on Tuesday its board has approved a plan to reincorporate from Bermuda to Ireland, and will ask its shareholders to approve it, becoming at least the third industrial company to move its incorporation out of Bermuda.

The electrical products maker cited the need to better manage its cost structure, including taxes and regulatory costs. Cooper said Ireland has a stable legal and regulatory environment and a solid network of tax treaties with trading partners.

Last week, Ingersoll-Rand Co (IR.N) shareholders approved a similar move from Bermuda to Ireland, and the next day Standard & Poor's said it would remove Ingersoll from its S&P 500 index, since Ireland-based companies are not eligible for inclusion in the widely tracked index.

Similarly, Tyco International Ltd (TYC.N) was removed from the S&P 500 in March when it reincorporated from Bermuda to Switzerland.

Cooper shares were down $1.57 or 4.4 percent at $33.95 in late morning trading on the New York Stock Exchange.

Cooper said it will remain subject to U.S. Securities and Exchange Commission reporting requirements and to corporate governance rules of the NYSE and it expects to continue trading there under the symbol "CBE." It will continue reporting results in U.S. dollars.

Index funds that would be required to sell their Cooper shares after reincorporation hold about 13 percent of shares outstanding, or about 22 million shares, according to Citi estimates.

"We believe the underlying reasons (for the move) are equivalent to Tyco's and Ingersoll's desire for a more stable tax jurisdiction," Citi analyst Jeffrey Sprague said in a research note.

(Reporting by Nick Zieminski, Editing by Maureen Bavdek and Gunna Dickson)