The egg that Togepi was inside was taken care by Brock mostly but once Togepi hatched, the first thing it saw was Misty and so this was imprinted in its mind. Ash, Brock, Misty and Meowth all had a battle to see who would keep Togepi but even though Ash won, Togepi would only want to be with Misty as she was the first person it saw.
Misty's Togepi turned out to be a very stuck up and jealous Pokémon. It was rarely recalled back into its Poké ball and Misty carried it around in her arms everywhere she went. It is also a very curious and mischievous Pokémon as it wonders off quite often to check out things that get its attention often requiring it to be rescued from danger.
Misty's Togepi evolve into Togetic in the Mirage Kingdom and soon left Misty to look after the Pokémon there. Misty was sad to see it leave but realized that it had learned a lot and would be a good overseer.