I suggest you'd need to check with this the T&C's of the rental car company in Split. It is quite common practice for cars to be taken over the border so I shouldn't imagine it would present a problem.
Croatia is now in the EU but is not yet in the Schengen area, therefore the borders still remain.
The rental company's car insurance policy will definitely cover it, as both countries are in the EU, but whether the rental company allows you to drive abroad is a whole other issue, however it shouldn't be a problem with most agencies. Still a good idea to check before booking, though.
Thanks for the reply
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