Shortly after news that Rep. Gabrielle Giffords, D-Ariz., was shot at a local event in Tucson, U.S. Capitol Police Spokeswoman Kim Schneider said that USCP was on high alert.

"USCP remains at a high level of readiness, consistent with our operating condition on US Capitol Grounds. We continue to maintain a robust presence," Schneider said.

A senior Hill source tells Fox News that House Speaker John Boehner and his staff worked with the Sergeant at Arms, Democratic and Republican leaders.  

Initially many Hill offices expressed concern that there was no early guidance from Capitol Hill law enforcement about tightened security and any caution about coming to work, etc.

Later, the United States Capitol Police sent out the following notice:

The United States Capitol Police are directly involved in the ongoing investigation regarding the shooting of Congresswoman Gabrielle Giffords in Arizona. We are currently working with Federal, state and local law enforcement agencies.

While the United States Capitol Police does not specifically discuss the security of Members of Congress including details on our protective measures, the United States Capitol Police has communicated with House Members of Congress advising them to take reasonable and prudent precautions regarding their personal safety and security.

The United States Capitol Police remains at a high level of readiness, consistent with our operating conditions on U.S. Capitol Grounds, and we continue to maintain a robust presence.