Can a bank refuse to give smaller denominations if you do not have an account there?
If this means, can the bank pay you with a $100 bill instead of five $20 bills, yes. Banks are private businesses. They are not government organizations and have a lot of latitude. They have limited amounts of cash on hand and those denominations are limited as well. This is the case whether you bank there or not, but if the bank is low on one particular denomination, they'll certainly favor the needs of those who bank there over the needs of those who do not.
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