bbq

You need to find the particular rule/law and see how it defines a "terrace."

https://www1.nyc.gov/site/buildings/homeowner/barbecues.page found this, but not sure how this applies to garage roof/deck

"For apartment buildings or other residential buildings (called "multiple dwellings" in the Multiple Dwelling Law, it's illegal to store a standard backyard propane barbecue on a balcony, roof deck, roof, rear yard or courtyard. Standard propane barbecues use 20-pound liquefied petroleum gas – or LPG – containers. While propane tanks cannot be stored on roofs, you may use a propane tank that's smaller than 16.4 ounces for a short period of time on a roof. For a one- or two-family home, a propane barbecue grill is permitted — with no more than two 20-pound LPG tanks. See NYC Fire Code §307.5.3."

https://www1.nyc.gov/site/buildings/homeowner/barbecues.page

Now to add to the confusion as in your case, one man's terrace is another man's roof.
Your also thinking, everyone is cooking everywhere that I can see and that's true. Many are actually breaking the law.
When not in use you want it well covered, especially when the fire marshal does their yearly surprise inspection of the building. Have at least a fire extinguisher mounted nearby if you dont have a water source (hose).
Just to be clear I am not endorsing you having a propane grill. :)
You also have to judge on whether you want to take on the liability if you have a fire. Your insurance company may decide not to cover you, especially if you burn down you and your neighbors.

Did you bring it up tot the manager first or were you approached?
I only ask because if someone complained and they came to you, you should probably ditch the grill. If you asked, the manager was definitely thinking of their own liability.
Its the same with asking a fire marshal anything. They will always tell you need the extra fire exit, extinguisher, etc.

I think electric grills have nearly carte blanche but yeah, I know, might as well microwave it.

"For apartment buildings or other residential buildings (called "multiple dwellings" in the Multiple Dwelling Law, it's illegal to store a standard backyard propane barbecue on a balcony, roof deck, roof, rear yard or courtyard. " I would say that this propane bbq falls under the intent of the law even if they may be a loophole because the garage is not attached the actual dwelling building.

I took the risk of a propane gas griil on a small balcony on the upper east side for a few years - looking back it was blatantly illegal and not smart, luckily nothing ever happened. When I moved to midtown, despite having a large setback terrace, I did not take the chance. The one thing you might try is the Char Broil Electric Bistro grill - it meets the fire code and it does a halfway decent job - for me, it became an acceptable tradeoff, as opposed to the risk of propane.

We had a lot of problems with owners in a condo who refused to abide by the law for BBQ. We billed them for the fines we received by the fire department. We also had our attorney contact them about our insurance problems for the building over their BBQs. As a result, we added a bylaw prohibiting all types of outdoor cooking with exponentially escalating fines. We couldn't jeopardize the building over a few apartments that had terraces. People finally got the message.

Look for a butane powered grill and problem solved.

Goldie the law isnt specific for propane but for "open flame" grill.
Thats where the electric ones skirt the issue.
In addition, its a flammable gas which will enjoy the same rules and regulations for its transport and storage.

That obscure warning signon the long island expressway for commercial trucks carrying flammable and explosive gases and liquids applies to passenger cars carrying a single 20 lb tank of propane through tunnels.
$10,000 fine + if caught.

My husband got rid of our propane grill and got this Cookair grill, which runs on either batteries or electric, with wood chunks. It gets to 1,000 degrees , works really well with all meats, though I am not convinced it would do well with fish

There seem to be lots of sites that sell it but this dips the manufacturer's. Cookair.com
I post this while looking at our (propane) Firepit