Should I mention that my US visa application was refused when filling out my UK visa application?

If the Entry Clearance Officer (ECO) decides that you have lied on your application form the Immigration Rules directs them to refuse your application.   They have no discretion on this point.

Under the Immigration Rules your visa application will be refused where false representations have been made (whether or not it is material to the application) or where material facts have not ben disclosed.

If the ECO decides that you have lied and used deception in your application all future applications will be refused for the following ten years.

I can't tell you what will happen if you choose to disclose this information and answer the question truthfully.  However, the Immigration Rules dictate that a very tough approach is taken to those providing false information.  As Mark says, they hate lies on application forms!
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