I developed a .NET version of the API, currently I am reviewing it and documenting it before publishing it. There is a component of the API that I have already published, ENMFPdotNet. It is the component that fingerprints audio songs for querying their identification service. A NuGet package is also available here.
Since it is not the original utility you will have to roll out your own decoding process to 32-bit 22Khz monophonic PCM as this is the format that Codegen expects. I have put a small example on how to achieve that using BASS.NET, basically you submit a file name, specify the desired sample rate, the number of channels desired and you will get your audio data converted to that format.
Also, there is a workaround explained in the README on how to use the library in a Windows Store application.
If you prefer to use the original command-line utility (codegen), it is available here.