There is a generic form for this posted at
There is a much more comprehensive California form posted at
which would probably be acceptable in Connecticut with minor changes. This form has the advantage of specifically allowing you to get Medicaid on behalf of the child, if necessary. (They call Medicaid "MediCal" in California.)
The U.S. State Department has posted a form at
I am sorry I have been unable to find a similar form used in Connecticut.
The California form is adaptable to be used in any State.
Since they are not married, the mother is the sole legal guardian and custodian, and she can sign an appropriate paper giving you temporary custody. Many travel agents will have a suitable form.
You can get a free consultation from some of the family law attorneys listed by location here.
You should not have to go to court to become the temporary guardian, although you can get a court order appointing you as guardian if you want to waste money. You can save money by having a local attorney draft a suitable form, or you can modify the California form and have it reviewed by a local attorney if you wish.
I hope this information is helpful.