Applicability of Z Score to Financial Institutions
The Altman z-Score in unchanged form is not a suitable tool for banks and financial institutions as it was designed for trading companies and service companies. The formula in the z-Score is expecting factors like working capital (which banks don't have in the traditional sense), and the sales/assets measure for a bank is significantly different against a trading company.
For banks, you are best to examine things like their grading for bonds, or their portfolio, or the return on tier-1 capital, or the prices for the credit-default swaps.
Of course you can use Altman's thinking, for example to compare the financial position of banks in one country or sector and to predict which ones are at risk. However you need to make modifications to accommodate the immense complexity of financial institutions.