Police in California are investigating how an audio file stored in Governor Arnold Schwarzenegger's computer system was leaked to the news media.
Mr Schwarzenegger apologised with Bonnie Garcia at his side
In the recording Mr Schwarzenegger refers to Hispanic Americans as "hot", with "black blood in them".
A campaigner for his Democratic rival said her staff downloaded the file but did not know how the media came by it.
Mr Schwarzenegger has apologised for the incident, which comes two months before state elections.
The Los Angeles Times published excerpts from the recording on Thursday.
Mr Schwarzenegger and his chief of staff can be heard speculating on the ethnicity of state Republican legislator Bonnie Garcia, wondering whether she is Cuban or Puerto Rican.
Mr Schwarzenegger then says: "They are all very hot. They have the, you know, part of the black blood in them and part of the Latino blood in them that together makes it."
A chastened Mr Schwarzenegger apologised for the remarks and said he had cringed when he read them.
The inspiration for the remarks, Ms Garcia, said she had not been offended and that they had been taken out of context.
Cathy Calfo, the campaign manager for Mr Schwarzenegger's Democratic rival for governor, Phil Angelides, told the Sacramento Bee newspaper her staff had downloaded the digital audio file.
But Ms Calfo said she did not know if the Angelides campaign had given the recording to the LA Times.
She said her campaign had done nothing inappropriate and that the file was openly available on the governor's website.
Mr Schwarzenegger's legal adviser disagreed.
Andrea Lynn Hoch said the download was unauthorised and taken from a password-protected area.
She said computer records of the access had been given to state police for their investigation into whether a hacker broke into the governor's computer server.