I've looked through posts and can't figure out why tax is not being calculated.

The situation is:
I want tax calculated for all sales billed to customers in Connecticut.

My tax settings are:
Prices include tax:        False  
Allow customers to select tax display type:  False
Tax display type:        Excluding tax
select Display tax suffix:      False  
Display all applied tax rates:      False  
Hide zero tax:          False  
Hide tax in order summary:      False  
Tax based on:          Billing address
Country:          United States  
State / province:        Connecticut
Zip / postal code:        Null
Shipping is taxable:        True    
Shipping price includes tax:      False  
Shipping tax class:        Taxable
select Payment method additional fee is taxable:False  
EU VAT enabled:          False  

Default tax provider:  Tax By Country & State & Zip
Only tax rate for Tax By Country & State & Zip is "Taxable"
and is set up as follows:
Country:    United States
State / province:  Connecticut
Zip:      *
Tax category:    Taxable
Percentage:    6.35

All product variants have:
Tax exempt:  False
Tax category:  Taxable

The way I understand it, once a customer with a billing address which contains State=Connecticut gets past the billing address portion of the checkout process they should see a tax added to any order of 6.35%. All others should see no tax.
Instead, tax is never calculated on checkout. I must have missed someting, but I can't see what. Any insight would be appreciated.