Does the "in" imply multiplication, in which case split in half is correct, or is it division? It sounds like the latter to me, but I've heard it used both ways.
They are both correct. If the focus is on the fact that I now have two objects, whereas before I had only one, I'd say split in two; if I want to stress that now each object is half the size of the single object I had before, I'd say split in half. In each case, though, the emphasis is so subtle that it would probably escape the conscious perception of the hearer, as indeed, the stress probably was not consciously calculated by the speaker.
I would rather split into halves or in half or into two, but not in two, neither into half.
From Oxford dictionary:
Divide or cause to divide into parts or elements. ‘The river had split into a number of channels’. ‘Splitting water into oxygen and hydrogen’.
‘It left me absolutely dumbfounded to see the 25-foot high walls, to see how towns have been split into two.’
‘He welcomed another measure now set to be adopted by the agency, under which the westbound carriageway will be split into two separate lanes.’
‘The development will be split into five separate blocks.’
‘Under the new scheme, the town centre will be split into 12 different zones which council bosses claim could be cleared in minutes.’
‘It takes energy to split the water molecule and release hydrogen, but that energy is later recovered during oxidation to produce water.’
‘The exam is split into 10 separate tests, which last from two minutes to 18 minutes.’
‘The water molecule is split into hydrogen ions (positively charged atoms) and oxygen.’
‘Classes, which last for 45 minutes, are split into separate sessions for babies, one- to two-year-olds, and two- to four-year-olds.’
‘This electricity splits the water molecules in an electrolyte, producing hydrogen.’
‘After much debate, it was split into two separate and distinct countries.’
‘This resulted in two items being added, no items being dropped, one item being split into two separate items, and one item having minor wording changes.’
‘The program is split into three separate phases.’
‘Her hair was pulled back into a large ponytail which was spsplit in halflit into five separate braids.’
‘But when did the Olympics split into separate Summer and Winter Games, and where were the first Winter Olympics held?’
‘The playing field is split into three separate areas: surface, air, and underground.’
‘The cotton country on this farm is split into two separate developments of about 1250 acres each.’
‘The flow of coolant when entering our heatsink base is split into six separate channels and two separate directions.’
‘The response was split evenly - 44 percent didn't work; 44 percent did work.’
‘The retail business of both his Florida and New Mexico stores was split evenly between new and pre-owned vehicles.’
‘Sozopol is split into two main parts: the old town and new town - known as Harmanite.’
Check out this answer too.
It literally means split (break or cause to break forcibly into parts - as shown here) in (how many parts?) half/two. Either of these is grammatically correct.