According to the three Madhaahib, viz. Shaaf?ee, Maaliki and Hanbaliy, Calamari is permissible irrespective of it being a fish or not.
However, according to the Hanafiyah, it will not be permissible on account of it not being a fish. It is Makrooh Tahrimi, which in reality means it is Haraam. (Takmilatul Bahr Vol.8 Pg.196, Raddul Muhtaar Vol.5 Pg.68-H.M.Saeed, Bahr Vol.6 Pg.187, Mabsoot VOl.11 Pg.255, Bada’i Vol.5 Pg.35, Tabyeen Vol.5 Pg.296 ,Fathul Qadeer Vol.6 Pg.421 and Vol.7 Pg.118)
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai