(CNN) -- An ugly Senate campaign in Kentucky grew even uglier Sunday as Democrat Jack Conway and Republican Rand Paul faced off in a debate that devolved into a name-calling session rather than a give-and-take on the issues facing the state's voters.

The debate at the University of Louisville came a day after Conway, the state attorney general, released a television ad questioning Paul's values.

"Why was Rand Paul a member of a secret society that called the Holy Bible 'a hoax,' that was banned for mocking Christianity and Christ?" the ad's announcer says. "Why did Rand Paul once tie up a woman, tell her to bow down before a false idol, and say his god was 'Aqua Buddha?'"

The ad, which is running statewide, is based on reports that Paul was a member of a secret society while a student at Baylor University. GQ Magazine and The Washington Post quoted an anonymous woman as making the claims in August.

The ad was an oft-repeated topic of debate from the start Sunday night as the Tea Party-backed Paul gave his opening statement.

"I'm disheartened that my opponent has chosen to attack my religious beliefs," he said. "We have serious problems in our country ... and he has descended into the gutter to attack my personal religious beliefs. ... Jack, you should be ashamed of yourself. You should apologize. Have you no decency? Have you no shame?"

It was a familiar refrain as Conway pressed Paul to explain his alleged involvement in the group while Paul shot back with such quips as, "You know how we tell when you're lying? When your lips are moving."

Despite the controversy, there was some talk of the issues at stake in next month's elections -- the economy, health care, job creation, illegal immigration and the war in Afghanistan -- though the candidates stuck to general positions on most subjects, perhaps because of the debate's format that allowed the candidates little time to answer.

On the government bailout, Paul said he believes it was a "mistake." "I believe our problem is a spending problem, not a revenue problem. The priority needs to be given to balancing the budget."

On illegal immigration, Conway said there aren't enough agents to curtail the problem. "I want to work on a system that's tough, sensible and fair."

On health care, Conway declared that "We need to fix the health care law," while Paul said he would "get rid of the whole thing and start over."

But the debate's agenda remained the same for both candidates: Conway attacking his opponent's positions on cutting government programs and Paul accusing Conway of making up those positions.

"It's hard to argue with him because he makes up my positions and then I have to debate made-up positions," Paul said.

At one point, Paul threw up his hands and said, "I give up. How do you argue with somebody who has no logic and makes no logical sense? ... It is absolutely absurd. To have a conversation with you, you demean the state of Kentucky and you embarrass yourself."

Paul wasn't the only one dishing out barbs, however. Conway told Paul, "You don't have the guts to stand by your positions."

The debate ended much the same way as it began: "When this debate ends, you'll notice that I will not be shaking his hand tonight," Paul said in his closing statement. "I will not be shaking hands with someone who attacks my religion."