The animal that is commonly associated with Athena is the γλαῦξ (glaux), which is often translated simply as 'owl', but actually refers specifically to the Athene noctua. See for example the γλαῦξ entry in the Liddell & Scott Greek–English Lexicon, which also gives several references to authors mentioning the γλαῦξ and its association with Athena. Among those, several quotes by Aristophanes, like
But the strongest proof of all is that Zeus, who now reigns, is represented as standing with an eagle on his head as a symbol of his royalty; his daughter has an owl [γλαῦχ᾽], and Phoebus, as his servant, has a hawk.
Aristophanes Av. 516 (greek/eng)
I have seen Athena in a dream, pouring out full vials of riches and health over the people.
I too have seen the goddess, descending from the Acropolis with an owl [γλαῦξ] perched upon her helmet; on your head she was pouring out ambrosia, on that of Cleon garlic pickle.
Aristophanes Eq. 1093 (greek/eng)
The certainty that the γλαῦξ was the Athene noctua and not another kind of owl comes from the precise descriptions that came to us from many different authors. For references, see the 'Glaux, Glaukos' entry in Birds in the Ancient World from A to Z by W. Geoffrey Arnott:
The Little Owl (Athene noctua), which was clearly distinguished by Alexander of Myndos (fr. 11 Wellmann) from the similar Skōps [the Scops owl] as slightly bigger (21–23 cm ~ 19–20 cm: cf. also Aelian NA 15.28) and clearly bulkier, with large yellow eyes and a face dominated by a white fringe (cf. Cyranides 1.3,
3.10) and a frowning expression.
Its familiarity led to many accurate descriptions and comments in ancient authors: a predator (Aristotle HA 592b8–9) that fed on mice, lizards, beetles and locusts which it hunted primarily at dusk and around dawn (HA 488a25, 619b18–23, Aristophanes Birds 589, cf. Longus 4.40, Pliny HN 29.92: in fact as a nocturnal hunter it takes a rest between midnight and 2 a.m.)[...]
Page 45 of A Glossary of Greek Birds by D'Arcy Wentworth Thompson also gives a comprehensive list of references on the γλαῦξ.