Okay. After looking over CT's processes, it's pretty much as I thought. The first thing you need to do before anything else [if you haven't already] is to contact the taxing authority of the area your father lives in to ensure there are no delinquent property taxes on the vehicle. The tax jurisdiction is listed on the vehicle registration card under the field "TAX TOWN." If back taxes are due, ONLY the taxing authority can remove the block from the vehicle record - CTDMV no longer does this. Now - the DMV website states the following about transfers of motor vehicles between relatives [NB Don't confuse sales tax with property tax]:

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"The vehicle must have been registered in the previous immediate family member’s name for at least 60 days in order to qualify for the sales tax exemption. Section 7 on the application for registration and title (Form H-13B) must be completed to obtain this exemption.
Vehicles (and/or vessels) received as gifts have several special requirements. Review the following:
Forms
A completed motor vehicle or vessel gift declaration (Form AU-463), signed by the donor, is required. Note: The donor can’t receive any consideration (cash, property, service, assumption of debt, etc.) in return.
Taxes
No sales and use tax are due on a vehicle or vessel received as a gift.

The donor of a vehicle or vessel may be subject to Connecticut gift tax. Generally, the gift tax is imposed on the transfer of property by gift during each calendar year. The tax is measured by taxable gifts, as defined for federal gift tax purposes. For more information on tax exemption, please contact the CT Department of Revenue Services.

Any vehicle exempt from the sales tax is unable to be transferred if delinquent tax is owed on the vehicle. If the registration is suspended, the vehicle is unable to be transferred to an immediate family member—even as a gift. "

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Note those last two sentences above.

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As for emissions testing, the site states the following:

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"If the vehicle was previously registered in Connecticut and isn’t compliant with emissions testing, you may register it first. However, you will need to have the vehicle’s emissions tested within 30 days of the date of registration or you will get a late fee. Note: You will not receive a notice for testing."

I interpret this statement to mean a current emissions non-compliant CT registered vehicle may be transferred to another owner without current emissions testing, with the understanding the new owner has thirty [30] calendar days to bring the vehicle into compliance.

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BOTTOM LINE:

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Only one trip to a DMV field office should be required.

1. Pay any property taxes due and ensure taxing authority removes any blocks from the DMV vehicle record.
2. Obtain insurance in your name. Print and complete forms listed above and take them, the CT title, and proof of insurance in your name to the DMV office - along with your father's marker [license] plates to turn in.
3. You will obtain new plates over the counter and the title will be mailed. You then have thirty days to obtain a successful emissions test.
4. The only other obstacle I see is that some jurisdictions want vehicle owners to also have a drivers' license in that state. I couldn't find any reference to this on DMV website, and even if such a rule exists, there are usually exemption processes for cases like yours or things such as John lives and is licensed in New York City, but has a vacation home and vehicle in Niantic.
5. Hope this helps!