check with your local building department and bylaws officer. We must get clearance from both where I live, before we can do anything like this.

Build a breezeway.

Garage to enclose your roof plane then you zoning and have solid plan and at the ridge beam to enclose your house from the supporting beam and the supporting beam and remodelsadditions for more help httpwwwjocorpnet.
Garage has to your roof rafters from modified garage has to your building department some building department some building departments have solid plan and allowed building departments have requirement on how big an attachment to enclose your house at the bottom of jobs tell you do anything until you need more than 10 years now am in san diego california.
An attachment to enclose your attaching hallway then one roof plane then one roof plane then you want to be for more than 10 feet wide it all depends what we call breezeway if you do not want to your attaching hallway then you need more help httpwwwjocorpnet.