Rep. Darrell Issa (R-Calif.) plans Thursday to demand a vote to subpoena the records of Countrywide Financial’s controversial Friends of Angelo mortgage program, a request that threatens to complicate Connecticut Democratic Sen. Chris Dodd’s reelection bid by refocusing attention on the company’s VIP mortgage scandal.

Dodd, who was cleared by the Senate Ethics Committee in August of any wrongdoing in a complaint alleging he received a special mortgage deal from Countrywide, has seen his poll ratings improve considerably in recent months. But Issa’s continued push for a deeper investigation is reviving the issue, providing fodder for the crowded field of Republican opponents.

“It’s one of the central issues — this and the many other Dodd scandals,” said Jim Barnett, campaign manager for former Rep. Rob Simmons, the GOP front-runner in Connecticut...