In documents obtained under the Freedom of Information Act, it has been learned that the US Department of Justice investigated Barack Hussein Obama and in particular looked at his whereabouts around 1961.
Details appear on page 7 of the 182-page report. Following is an excerpt from the report (click to enlarge).
This US Department of Justice investigation shows Barack Hussein Obama (President Obama’s father) last entered the United States on August 9, 1959. The investigation conducted in 1964 demonstrated that Mr. Obama, Sr. was in the United States continuously between 1959 and 1964, precluding a trip to Kenya in 1961. While this does not prove that Stanley Ann Obama herself did not travel to Kenya, it makes this scenario even more wildly impossible.
In an interesting side note, we see that the route traveled by Obama from Kenya to the United States in 1959 included a London to New York leg, where Obama Sr. entered the United States (see Page 10).