Does refinancing the mortgage with the same bank but with a larger loan need a new title insurance?
At least in Ohio, the answer is yes. A new loan policy of title insurance is needed by the lender because they want to be insured up to the new loan amount. If this refinance is within 10 years of the date you initially took out the loan, your title company may be willing to give you a "re-issue rate", which is about a 30% discount.
You need to ask your lender. If they are re-writing the existing loan, they may simply ask for upgraded Mortgage policy and have you pay the difference for the new loan amount based on the local rates/fees.
If you are paying off the existing loan, then they will require a new Mortgage Policy. You must remember that a Mortgage Policy is only good for the life of the loan, so once it is paid in full (even from a refinance with the same bank) the mortgage title policy ceases to exist.
Most states offer a refinance rate which is calculated on the new loan vs the original amount of the current loan.
The above answer is pretty thorough - just check with your lender/local title agency to find out what the fees are for your state.