By Mary Wisniewski
MADISON, Wis (Reuters) - Former Wisconsin governor Tommy G. Thompson, a Republican, filed a statement of candidacy with the Federal Elections Commission on Tuesday for the U.S. Senate.
Thompson wants to fill the seat being vacated by retiring Senator Herb Kohl, a four-term Democrat. Thompson had already announced his intention to run for the seat last month.
According to his campaign, a "formal announcement tour" is in the works but the FEC filing was the next step in Thompson's organization efforts for a Senate campaign.
Wisconsin, which fought a highly partisan battle over public sector collective bargaining rights this year, is expected to be a battleground in 2012, when Democratic President Barack Obama runs for reelection.
The state backed Obama when he won the presidency in 2008, but is now considered a "swing state," not seen as heavily favoring either party.
The Wisconsin seat Kohl is vacating was also being contested by Congresswoman Tammy Baldwin, a Democrat and one of the few openly gay members of Congress.
Other Republican contenders are former Rep. Mark Neumann and Wisconsin Assembly Speaker Jeff Fitzgerald, who led the fight to curb public worker union rights.
In a statement from his campaign, Thompson touted his tax and spending cuts as governor.
"Barack Obama and Harry Reid have a vastly different idea for your hard-earned money," Thompson said. "They want more and more and more. But I will fight them every step of the way."
Democrats in 2010 lost a long-time Senate seat held by the party when former Wisconsin Democratic Senator Russ Feingold was beaten by Republican challenger Ron Johnson. Feingold has decided not to run for any office in 2012 but will stay in academia.
Republicans need to gain just three seats in the 2012 Senate elections to take over majority control of the upper chamber.
Thompson served four terms as governor and then as Secretary of Health and Human Services during the George W. Bush administration.
(Additional reporting by Jeff Mayers; Writing by Mary Wisniewski; Editing by Jerry Norton and Cynthia Johnston)