Story highlights Sen. Rand Paul says the scanner didn't go off the second time he went through

"Is it too much to ask to have a little dignity when you travel?" he says

Paul refuses a pat-down at a security checkpoint in Nashville after setting off an alarm

The TSA says those who set off alarms "cannot be granted access to the secure area"

Authorities blocked U.S. Sen. Rand Paul at Nashville International Airport on Monday after the Kentucky Republican refused a pat-down at a security checkpoint, his spokeswoman said.

Paul told CNN that he went through a scanner at the airport and set off an alarm. He wanted to go through the body scan again instead of getting a pat-down -- claiming that he showed Transportation Security Administration officers his knee and under his socks -- but the agents refused his request, according to the Kentucky senator.

"When an irregularity is found during the TSA screening process, it must be resolved prior to allowing a passenger to proceed to the secure area of the airport," TSA spokesman Greg Soule said. "Passengers who refuse to complete the screening process cannot be granted access to the secure area in order to ensure the safety of others traveling."

The senator said that he didn't think it was "appropriate" for him to have a pat-down, adding he should have been able to go through the scanner again.

"Is it too much to ask to have a little dignity when you travel? And shouldn't an adult be able to get back in line and go through the scanner?" he told CNN. "I don't think that's too much to ask."

A TSA official said Paul was "not detained at any point" and left the checkpoint willingly. The official was not authorized to speak for attribution.

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Paul said he was "ejected" from the screening area and told he may be subject to a "full body search" after he began talking on his phone. He was eventually rebooked on another Washington-bound flight, saying that time the screener did not go off when he went through it.

"It tells me that either the machines are inadequate, or they are not telling us the whole story," said Paul, insisting that two TSA agents told him that the screeners go off randomly -- an assertion the federal agency denies.

One of the most conservative members of the Senate, Paul is an outspoken critic of what he characterizes as an overly obtrusive federal government threatening to strip citizens of various rights and civil liberties.

During a Senate hearing with TSA Administrator John Pistole in November, Paul argued that the TSA policy of letting children go through the full-body scanners twice -- rather then be subjected to a pat-down -- should apply to adults as well. He predicted that with such a policy, "you'll get rid of a lot of the anger and animosity towards the TSA."

On Monday, the senator said he also supported some sort of "frequent traveler" program -- so that people who travel often aren't as likely to be subject to pat-downs -- and "selective risk assessments done on people are international travelers (and) people who have ties to groups that may be terrorists." He added that someone in the screening area should have "discretion" to decide, on a case-by-case basis, if a pat-down is necessary.

"I think we've gone overboard ... I feel that our dignity is compromised, but I don't feel more safe," said Paul, noting he spoke with Pistole after the incident Monday. "Regular, ordinary citizens don't need to be put through this, particularly the frequent travelers."

Rand Paul is the son of libertarian Texas Rep. Ron Paul, a candidate for the Republican presidential nomination. Ron Paul weighed in on the controversy Monday afternoon, calling it an example of a "police state in this country" that "is growing out of control."

"One of the ultimate embodiments of this (police state) is the TSA that gropes and grabs our children, our seniors, and our loved ones and neighbors with disabilities," the congressman said in a written statement. "The TSA does all of this while doing nothing to keep us safe."