393-On-The-Road answered it best, there are outside areas for smoking.
Sorry I can't help. Non smoker so not something I check.
Short answer: No, certainly not in any guest rooms or public areas.
Longer answer: You can go outside in the parking lot, and maybe you can smoke in the inner courtyard around the pool, but I doubt it.
I didn't see anyone smoking.
Marriott prides themselves in being a smoke free environment and established this policy in 2006.
However, Although smoking is not permitted within hotel buildings themselves, guests who smoke are permitted to do so outside in designated areas.
Get an answer from Courtyard New Haven Orange/Milford staff and past guests.