This is a question commonly asked by those looking to make their first foray into the multisport world. USAT rules provide a very technical answer to this question. The USAT Rules Education helps to decipher some of them.
We'll provide a checklist here that should help.
-the bike must have brakes that work on both the front and rear wheels. USAT Bike Brake Rule
-The bike must be in good working order. You may think that taking your $60 bike in for a $65 tune up is ridiculous. Consider it an investment in your safety, fitness and overall enjoyment in riding. USAT Bike Safety Rule Remember to take it in a few weeks before the race. The shop will get very busy in the last week as we all procrastinate.
-The bike must be able to roll forward while the pedals remain stationary. IE, it has to be able to roll without the pedals rotating. "(k) There must be a free-wheeling mechanism between the crank and the rear wheel that allows the bicycle to roll forward while the pedals remain stationary."
-Check your bar end plugs. Not having them is a big no no and is easy to fix! USAT Bar End Plug Rule
If you met this criteria, you bike is most likely legal! Still question whether you can race on it or not? Contact the Race Director. They are certified and can answer your questions. Again, it is best to ask them a few weeks before the race. They will most likely be extremely busy and somewhat stressed out right before the race and may not be able to answer your questions in a timely manner. Race, be safe and have fun!