Though there are only 3 parts in the song, the texture varies quite considerably.
At the beginning the texture is monophonic because only the bass guitar plays.
From bar 4 (0'16) and for the majority of the song the texture can be described as melody and accompaniment or homophonic. This is because, though the acoustic guitar and bass are very active, playful and somewhat independent, they are less so than the vocal melody, which sings the principal tune.
An exception to this is the start of the third verse at bar 88 (3'35) which is polyphonic. The voice sings Vocal melody B whilst the bass plays Vocal melody A in the accompaniment.
At the start of the bossa nova in bar 19 (1'10) the bass plays parallel 3rds. This seems to be the only example of any parallel motion in the entire piece; for the majority each part has an autonomous role which injects much energy and excitement into the music.