I have a construction mortgage loan. The bank states I need to pledge a $50,000 certificate of deposit to provide extra collateral. Can it do that?

You need to refer to your loan agreement. Any requirement for assigning or pledging additional collateral during the construction term would have been disclosed in the agreement.

Typically, this happens when there is a loan-to-collateral value shortfall. The bank requires the borrower to pledge another asset to remedy the shortfall.

You should contact your lender for an explanation.