"Bush will get his," Smith screamed as he was taken into custody, according to federal court documents..
"I'm going to work for George W. Bush and the Pentagon," the note said, according to US officials. "I have to slay a dragon and then Barbara Bush is mine."
When asked about his marital status, the man said: "I'm divorced and not currently seeing anyone, but I am working on a relationship with Barbara Bush," court documents show.
At a preliminary hearing, Assistant Attorney Andrea Griswold said the government believes Smith was referring to Mr Bush's daughter and not his mother, who is also called Barbara.
It is a crime under US federal law to threaten a current or former President.
Smith's defense lawyer, Peggy Cross-Goldenberg, said the note and Smith's outbursts did not constitute a "true threat."
"As far as I can tell George W. Bush is not in New York City," she said. "It would be different if we were in Texas near George Bush's ranch."
The judge also conceded it was "unclear" a jury would find Smith guilty.
"Admittedly, there is some inconsistency in the notion that the way to win Barbara Bush's affections is to kill her father," US Magistrate Judge Henry Pitman said.
- UK Independent