A new poll conducted for the Club for Growth showed Sen. Dick Lugar (R-Ind.) and his primary challenger, state Treasurer Richard Mourdock, in a statistical dead heat.

Mourdock had a small advantage over Lugar, 34 percent to 32 percent, in the Basswood Research poll released Tuesday. But Mourdock’s 2-point lead is within the poll’s 4.4-point margin of error.

The conservative, anti-tax organization has not endorsed Mourdock, but the Club for Growth President Chris Chocola has frequently criticized Lugar’s record. Earlier this month, the club sponsored television advertisements blasting Lugar across Indiana.

“An incumbent who sits at 32 percent in his own party’s primary, and trails a much less known challenger, is in a world of trouble,” Chocola, a former Indiana Congressman, said in a statement. “Senator Lugar is a very decent man, but it’s clear from the poll that after 35 years, Hoosier Republicans are eager for a more conservative alternative.”

About one-third of those polled, 34 percent, said they were undecided about the GOP Senate primary field.

Basswood Research conducted the poll of 500 likely Republican primary voters July 23-24.