I think she started to develop an "attachment" to him in catching fire, she got to the point where she needed him to sleep with her just so she could sleep! And in the arena she opted to save Peeta instead of herself. Only in Mockingjay when he was taken away from her and tortured and brought back did she realize that she could not live without him! A much deeper emotion than just actor loving someone,she cared so much for him she was willing to die for him! She was crazy for him!!
There's no true time in the livres when Katniss comes out and says she loves Peeta (the closest we get is at the end of Mockingjay when she says, "Real.") Through out, she does shows how protective she is of him.
I started believing that Katniss was falling in l’amour with Peeta in Catching Fire, when she decided to save him in the Quarter Quell even though it'd mean her own death. I don't think she realised herself until Mockingjay, though.
I think Katniss start l’amour Peeta when she decided to protect him in first book, at the 74 edision of the Hunger Games ( when she discover him at that river). But she don't realize in that moment, just when he was caught par the Capitol.
