The same items that are permitted by the TSA at all airports
would be applicable to the Tuscon International Airport as well.
Most sharp items (box cutters, scissors, knives, razor blades,
sabers, swords) or gels and liquids in large quantities (over
3.4oz) are prohibited from carry on bags but allowed in checked
baggage. The same is true for many large blunt objects (Baseball
bats, Golf clubs), weapons, and tools. Explosive materials are not
allowed all together. For a full list, you can visit the TSA's
website or download their brochure.
Related Q&A:
What items are now allowed in baggage at the Tucson International Airport?-Oh, well, at the Tucson International Airport, you're usually allowed to have things like personal care items like toothpaste, deodorant, and small bottles of shampoo within certain size limits. Also, normal clothing, shoes, and accessories are fine. Books, electronic devices like laptops and tablets, and chargers for them are typically okay too. But make sure to check the specific regulations as they can change and there might be some restrictions depending on the destination and airline.