Is there a tax concern when changing banks for a CD IRA?

In general:

If you want to move an IRA to a different custodian, that is a rollover.  You can do this yourself, where you get a check, and send it to the new bank within 60 days.  This is an indirect rollover and you can only do that kind of rollover once per year.   Or, you can set up a direct electronic transfer between the two custodians.  That is a direct rollover and there is no limit how many times you can do this.  A properly completed rollover does not create any taxable event.

However, specific to a CD:

You may need to contact your current bank.  If you are holding your IRA in the form of a CD, and you want to do your rollover before the CD matures, you may have to pay a penalty for cashing in the CD early.  (It is likely that you have to cash in the CD, move the cash, and then buy a new investment.  It is unlikely that you can move the actual CD.). Paying the penalty is not taxable or deductible, but it means there will be less money to invest in the new IRA.  (With a Traditional IRA, you only pay tax when you make a withdrawal, and you pay tax on whatever you withdraw.  If you lose money on investments, you don't get a tax deduction ever, it just means you pay less tax when you withdraw because there is less to withdraw.)