I am trying to tell someone that I'm currently reading a book, but I haven't finished it yet. I thought that I should use przeczytać to express this fact.
Czytam książkę ale nie skonczyłam jej jeszcze czytać.
The Imperfective form, czytać, is used here. You are currently reading the book, so this is present tense and therefore not perfective.
My Polish grammar is far from perfect, so you would be better taking advice from someone Polish I think.
Please look at the threads I linked you to though. In the first one the OP is asking the same question as you.