TBH, I have no idea about OrangeHRM's API. But I had a bit of a google and here's what I found:

My first question is have you initialised it? I.e. following the steps noted in their wiki? Apparently it doesn't work until you do that...

Also, there is an open issue on their tracker which is somewhat similar. Whilst it's not quite the same as what you've reported, looking through that thread, there seemw to be a number of others hitting the same issue as you (e.g. this guy). So I suggest having a read through that.

Finally, I noticed that right at the top of their API docs, there is a somewhat ominous message which I don't completely understand:

This documentation intended for OrangeHRM Professional and Enterprise versions. OrangeHRM Open Source will not be supported by these APIs

I'm not really clear whether that means that the open source build doesn't have the API at all, or whether it's incomplete, or that it's all there, just that they don't support it? So perhaps it doesn't even work at all?!

There is also a possibility that there is something missing from our build that is required to host the API. I don't think so, but I have had a careful look through the install docs again just to be sure that there was something that we missed previously. I can't see anything specifically related to the API at all, so am inclined to suspect that it should work...

If you find anything more out, please share as I'm sure it'd be useful for others...