Catalyzes the formation of 2'O-methylated cytidine (Cm32) at position 32 in tRNA. Is specific for cytidine. cytidine(32) in tRNA + S-adenosyl-L-methionine = 2'-O-methylcytidine(32) in tRNA + H(+) + S-adenosyl-L-homocysteine Homodimer. Belongs to the class IV-like SAM-binding methyltransferase superfamily. RNA methyltransferase TrmH family.