Yee, D-San Francisco, received calls on Monday from sheriff's detectives in Pima County, Ariz., where Giffords was among 19 people shot outside a Safeway store. Six people died in the shooting but Giffords, believed to be the target, survived.
"We haven't been updated on if there's a connection," Yee's spokesman Adam Keigwin said today.
Keigwin said Yee's office received threats relevant to Giffords' investigation in April 2010, when the senator helped reveal that officials at California State University, Stanislaus shredded documents related to Palin's contract fees as a keynote speaker.
During the incident, students dug through a trash bin outside a campus administration building and found a shredded contract with a speaker who required first-class air travel from Anchorage, Alaska.
Yee chided the university in news reports, and in response, several voice, text and graphic threats were sent to his office.
"Good thing you run in San Francisco 'cause you'd never make it anywhere else," said a sign-off to a voicemail that was preceded by substantial anti-homosexual comments.
Additional faxes and phone calls were overtly racist, both anti-Chinese and anti-black in reference to President Obama, Keigwin said.
No one's been arrested for threats made against Yee, which Keigwin said have happened for more than six years.
In one of the office's most notable incidents, calls to Yee's office said the senator was a "dead man" if he showed up to a 2005 news conference on violent video game legislation.
Keigwin received racist text messages again referencing violent video game legislation in 2009. Officers tracked down the person who made the threats and issued a warning, but no arrest was made, Keigwin said.
Keigwin said he didn't have a lot of information on how threats are typically handled because the California Highway Patrol manages the investigations.
The CHP and Pima County Sheriff's Office were unavailable this morning to comment on the investigation.