You'll want to identify the key of the song, and possibly the chord progression as well.
A common form of harmonies is 2 scale degrees below the original pitch. This is NOT the same as 2 semitones below a note. For example, in the key of C, the scale goes C D E F G A B C. The note 2 degrees below F is D.
If this note doesn't sound quite right, it could be clashing with the chord at that point in the song. Check what the chord is and try to find a harmony note that's in the chord, or sounds good with the chord.
This is much easier to do when you're still setting up the midi for the UST, because you'll be able to play all of the tracks together in a DAW to hear whether the notes sound good together or not. Although you could make harmonies just relying on music theory, the more important thing is going by how it sounds. After you've finalized the notes, you can then take that midi into UTAU for the final step of adding the lyrics and tuning.