I'm not familiar with your third party library, but you should be able to achieve the same with the built in methods, since it seems to be a simple synchronous request. Try this:
let url = NSURL(string:"http://localhost/project")
let request = NSURLRequest(URL:url)
var response: NSURLResponse? = nil
var error: NSError? = nil
let reply = NSURLConnection.sendSynchronousRequest(request, returningResponse:&response, error:&error)
let results = NSString(data:reply, encoding:NSUTF8StringEncoding)
// Continue your processing of results here...
Update
To use POST, employ an NSMutableURLRequest. General form is something like the following. The difficult to find part is NSURLProtocol.setProperty(...). See this page.
let url = NSURL(string:"http://localhost/project")
let cachePolicy = NSURLRequestCachePolicy.ReloadIgnoringLocalCacheData
var request = NSMutableURLRequest(URL: url, cachePolicy: cachePolicy, timeoutInterval: 2.0)
request.HTTPMethod = "POST"
// set Content-Type in HTTP header
let boundaryConstant = "----------V2ymHFg03esomerandomstuffhbqgZCaKO6jy";
let contentType = "multipart/form-data; boundary=" + boundaryConstant
NSURLProtocol.setProperty(contentType, forKey: "Content-Type", inRequest: request)
// set data
var dataString = "your data here" + boundaryConstant
let requestBodyData = (dataString as NSString).dataUsingEncoding(NSUTF8StringEncoding)
request.HTTPBody = requestBodyData
// set content length
NSURLProtocol.setProperty(requestBodyData.length, forKey: "Content-Length", inRequest: request)
var response: NSURLResponse? = nil
var error: NSError? = nil
let reply = NSURLConnection.sendSynchronousRequest(request, returningResponse:&response, error:&error)
let results = NSString(data:reply, encoding:NSUTF8StringEncoding)