In Death Note, Chapter 33 (Vol. 4), Misa Amane is arrested under the suspicion she was the Second Kira. After that, L said that they collected lots of evidences in Misa's room (the cat hair found on the video cassette, make-up powder, clothing fibers etc.), besides the fact the criminal who killed her parents was killed by Kira. Supposedly, the objects L was analysing in Chapter 32 (a hair, crumbs from a snack) were collected from her room.
However, how L became suspicious of Misa before seeing her in Chapter 32, in Light's university? I suppose he discovered the relationship between Light and Misa because Mogi saw when the girl appeared suddenly to Light in Chapter 31, and so L ordered an inspection to her room. So, is there any indication that he was him investigating every one of the Light's "girfriends" (including the "Refined Takada"), or it was just Misa that caught the attention of the detective?