( CNN ) -- Tiger Woods apologized on Wednesday for `` transgressions '' that `` let his family down . '' `` I have let my family down and I regret those transgressions with all of my heart . I have not been true to my values and the behavior my family deserves , '' he said in a statement on his official Web site . `` I am not without faults and I am far short of perfect . I am dealing with my behavior and personal failings behind closed doors with my family . Those feelings should be shared by us alone . '' Woods made the comments in a statement posted on his Web site the same day that a gossip magazine published a story alleging that Woods had an affair with a 24-year-old New York cocktail waitress . The nightclub hostess , identified by a supermarket tabloid as Tiger Woods ' mistress had called allegations that she is romantically involved with the golf superstar false and `` ridiculous . '' In an interview published Tuesday , Rachel Uchitel told The New York Post that a disgruntled acquaintance sold the story to the National Enquirer and that `` not a word of it is true . '' `` I work in clubs , and I am a businesswoman , '' Uchitel said . `` I do not have sex with celebrities , and I have not had an affair with Tiger Woods . '' Speculation has swirled around Woods since a wreck outside his Florida home early Friday left him with minor injuries and a citation for careless driving . The Florida Highway Patrol said Tuesday that its citation closes its investigation of the crash . Woods was not required to talk to state police about the wreck and did not sit for an interview with investigators . He issued a statement Sunday saying he alone was responsible for the crash and denouncing `` the many false , unfounded and malicious rumors that are currently circulating about my family and me . '' Opinion : Woods is only human . The 33-year-old golf phenomenon has won the Masters tournament and the PGA tournament each four times , as well as three U.S. Open titles . Investigators have said they do n't have details on why Woods was driving away from his home at such an early hour . A police report says the wreck was not alcohol-related . Uchitel said she has met Woods twice , once in her capacity as the VIP director at a club in Manhattan 's trendy Meatpacking District and another time through a mutual friend . `` That 's my job : to know these people , to have a relationship with them , to hang out with them , '' she told the Post . `` It does n't mean I am having sex with them or an affair with them . '' She said the allegations `` must feel horrible '' to Woods ' wife , Elin Nordegren . `` The worst part of it , it 's not true , '' Uchitel said .
NEW : Tiger Woods apologizes for `` transgressions '' that let his family down . By Michael Isikoff, CNN Senior Producer Updated 10:15 AM ET, Wed October 5, 2012