Bathroom faucet handle with no screws
There is no doubt a larger sized nut and washer around a threaded part of the faucet body that clamps up under the bottom of the rear sink shelf. Once any water piping is removed the nut and washer can be removed and the faucet lifts out from the top. 

On some there is just a washer and a retainer clip on the bottom side and then the skirt part of the faucet on the top screws onto the lower part and is tightened down from the top side.