Contract provisions that dictate where disputes can be handled (forum selection) and under which state's laws (choice of law) are fairly common when dealing with an out-of-state company especially with companies that do business in multiple states. Because they are making deals all over the country it is in their best interest to focus their legal representation in one place to avoid spending potentially large amounts of money litigating all over the country.
They can insist that this provision be part of the agreement between you two, however you are obviously not required to make the deal. If you were to sign this type of contract and try to challenge it later the reviewing court would most likely look to factors such as the relationship of the forum to the deal and the parties. In this case Connecticut is their home state but if all the work is being done in Arizona it might make more sense to litigate there, especially if all the witnesses and evidence were in AZ and it would be a financial burden to transport them to Connecticut.
The standard for getting these provisions thrown out is usually high and it must be shown that the contract or provision was unconscionable or so one-sided as to be oppressive. If you feel that you really would be unduly burdened if you had to litigate in Connecticut you should think long and hard before making this deal. A local lawyer may be able to assist you in negotiating an alternative forum or including provisions for paying travel fees to a prevailing party or requiring arbitration or mediation in a more convenient venue.
The above answer is not "legal advice" as specified under any pertinent rules governing the Professional Responsibilities of Lawyers and should not be relied upon. An attorney-client relationship has not been established by virtue of this correspondence. Legal issues are often complex and involve local laws and facts which may not be effectively communicated without a complete consultation.