Conn. Gen. Stat. § 42a-2A-708: Specific performance.

(a) The court may enter a decree for specific performance if the goods or the agreed performance of the defaulting party are unique or in other proper circumstances. In a lease other than a consumer lease, the court may enter a decree for specific performance if the parties have agreed to such remedy. However, even if the parties agree to specific performance, the court may not enter a decree for specific performance if the breaching party's sole remaining contractual obligation is the payment of money.

(b) The decree for specific performance may include terms and conditions as to payment of the rent, damages or other relief the court considers just.