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A licensed architect or structural engineer should be able to tell you what you can - by code and safety - build on top of the roof. It all depends on local codes and the existing structure of the roof.

Ask your building's management if you'll even have permission to construct first. If management says no, you'll be free from daydreaming about it altogether.

If you know the current square footage of the building you can look at the Department of City Planning website to determine the zoning in your area and what the allowable Floor Area Ratio (FAR) is. The FAR will let you know if you have any extra square footage to play with. If you don't you're out of luck but if you do you should contact an architect to determine what type of structure would be allowed by building codes and zoning.

I would check the building codes and ask a structural engineer. Roofs are built for wind and snow loads, whereas regular floors of a building are built for furniture, people, etc (dead and live loads). So a roof, in theory, does not need to support as much force as the rest of the building. With that said, I know people build greenhouses or put in hot tubs or whatever else on roof tops, so I'm sure it can be done, but yeah, definitely check with somebody first.

Access to the rooftop is different than owning the rights to build on the rooftop so check your deed and with your management company first. In my building, the people on the top floor ended up building on the roof and the buildings department decided that it was technically another floor to the building. The building's certificate of occupancy was revoked until the firestairs were extended up to the roof. The whole thing has been years of legal headaches and a huge money pit for the building.

I'd be sure to ask your coop board or management company before spending a nickel on an architect or structural engineer. If it's a coop, the corporation (i.e. the coop board) will ultimately control your ability to do anything. If the corporation that owns the building does not want construction on the roof, then it won't matter what the zoning rules/ DOB might theoretically permit you to do. I have a friend who learned this the hard way and ended up selling and leaving because her board would not permit any construction on the top of the building (a three story townhouse).

Well, if it comes down to it and The Man (gov't or coop board) won't let you build, you could always rig up tenting and lighting on temporary poles, add some outdoor furniture and area rugs and viola! Your very own Shangri-La! Potted plants and extra seating would also add to it. Don't let "no building on top of the roof" stop you from being creative.

Usually things that ARE permanently attached are the ones that are no no's. I might also mention that roofs are NOT meant to be walked on, and that you must install some type of roof decking no matter what. If you don't you will prematurely damage the roofing membrane and your co-op will hold you responsible, and the water will leak in "your apt" first. I know all this firsthand as I was on the board of a building where a tenant climbed out the window as access, to a landing and used this as additional space. she ended up doing $225,000 worth of damage, because the roof needed replacing and leaks.. You must put down either concrete tiles made especially for roofs or wood tiles.. this spreads the pressure of objects on top of it. This is better anyway since it would give a surface to attach non permanent things too. whatever you do never put a chair on a roof, a high heel is a killer too !!!
hope this helps
I also have 2 resources for you to use.. and
I also saw a great Pergola at BJ's wholesale club (huge) that you could put curtains on sides to create a private room. It was cheap 600 or so dollars, and can be disassembled, so no issue, except roof pressure..

One other thing I forgot, there are codes as to how high the side walls of the roof need to be, for safety.. I think it's 4 feet high, so you may also have to put up fencing for safety, else it's "your liability" if a drunk friend sits on the edge and falls off. so before you have you next party, even without any construction. NO heels No drinking, no sitting on side walls. NO FUN!!!!

You could also use rubber roof pads to help protect the roof membrane, may be a less costly alternative to concrete or wood. I echo the comments to check with management and then a structural engineer or architect. Also anything you build be it a new room or a tent should be attached without puncturing the existing roofing unless you have a plan for flashing and protecting the opening. Even then I would consider it much to risky as you could end up with a leak that would require complete replacement and big bucks.

Having just gone through this--

There are three issues: 1. Private agreements that restrict building rights; 2. Zoning or other legal barriers; and 3. Engineering barriers.

Assuming your coop/condo/building ass'n allows it, check with your permit office. THey will either tell you if zoning allows for it or refer you to the zoning board. Often, zoning rules restrict height, so look around and see if neighboring buildings are higher than you plan to build, as an indication. Then, you need to know the load capacity of the building and roof, which unfortunately requires an engineer (mine charged $3000).

I don't think it matters whether you are building a room/house or a shed; all 3 things are issues. You should be prepared to spend. We were putting a prefab 6x8 metroshed on our greenroof, over the stairway access, and the project was so expensive that we just opted for a skylight hatch and pull-down steps instead. (I'll save you 100 hours: www.insula-dome.com).

Good luck, it's an awesome roof and could be a cool space. Maybe consider a greenroof with patio like we did; kind of an outdoor patio/living space that also does the city some good.

if all the above works out, check out :

http://www.toppenthouse.com/

they do custom modular, crane lifted, roof additions in nyc. i saw them on tv and evidently it is cheaper and easier then going from scratch on site. they should be able to answer permit and code issues.

i'm not in nyc, but a friend tells me there are several firms doing these there now.