Maxxis is the official tire sponsor of the Tour de Park City. The Race and Super Century course travels over 5.75 miles of hardpack dirt. No we are not talking about a nasty gravel road. Each year Summit County applies a coating of magnesium chloride to the dirt section eliminating dust and 85% of the loose rocks.
This is still dirt though and riders in the past have flatted because they have ultra light race tires on their bikes.
We talked with the folks at Maxxis and they reccomend two tire options.
The first is the Columbiere.
The Columbiere is designed for the true road racer. The Columbiere’s slick design, with subtle siping, allows racers to cover ground in any conditions with plenty of confidence. 
Grooved slick design - front or rear
2-ply nylon breaker for increased puncture resistance
Pro road competition tire

Grooved slick design - front or rear
2-ply nylon breaker for increased puncture resistance
Pro road competition tire
The second tire is geared more for training but Rhett who is my partner in the Tour de Park City has put 6,000 miles on a set without a single flat!
The Re-Fuse is our second choice.
Maxxis' most popular training tire- providing excellent traction, durability and plenty of road miles in any condition. The Kevlar® belt and silkworm cap ply combine to provide a tire that Re-Fuses to puncture.

Diamond knurled slick design
Kevlar belt and silkworm cap for maximum puncture resistance
Training tire.

Diamond knurled slick design
Kevlar belt and silkworm cap for maximum puncture resistance
Training tire.
Either tire option will give you a solid tire that won't let you down when you hit the dirt section on the Tour de Park City course.
Here are the links to both tires:
Check out all the tires at www.maxxis.com