Rep. Jan Schakowsky (D-Ill.) released a poll Monday that tested her potential Senate candidacy, and the results showed her in a statistical dead heat with state Treasurer Alexi Giannoulias (D) in the February 2010 primary.

The six-term Democrat led Giannoulias, 24 percent to 22 percent, with 36 percent undecided. Giannoulias is the only announced candidate in the race so far, after former Commerce Secretary Bill Daley (D) announced last week that he would not run.

The poll is a sure sign that the Northside Chicago Democrat is seriously looking at the race. She told the Chicago Sun-Times, which first published the poll, that she will decide by June 8 whether she will run for the Senate or re-election to her House seat.

Appointed Sen. Roland Burris (D-Ill.), who has not announced yet whether he will seek a full term, scored 18 percent of the vote in the poll. Burris was appointed to the seat by former Illinois Gov. Rod Blagojevich (D), who was indicted on 19 counts of corruption earlier this month.

Schakowsky paid for the Lake Research Partners survey, which took the opinion of 600 likely Democratic primary voters from April 19-22 and had a margin of error of 4 points.

At the end of March, Giannoulias had banked $1.1 million. Schakowsky reported having $397,600 in her account at the end of the first quarter of this year.