During my last internship, I took an open source tool and enhanced it as a part of my project. Because of my growing interest in that tool, I took it home and added some more functionalities to make it more useful for others outside and then thought of publishing it.
The original source code is available in public domain without any restrictions, but since I worked on this tool during my internship, I wanted to know whether I have to take permission from my employer before publishing it.
Although I want to publish it, my mind tells me NO, as the code is now a property of my employer.
Edit 1:
This is what the original tool writer says about the code: "This code is released into the public domain without restriction"
Yes, if you changed it as part of your work for a company, then it is that company that owns the copyright for what you do. So you cannot publish your changes without permission from your employer. If you were modifying a freely available tool, though, you may want to ask your employer for permission to publish the code; many employers will allow this if it wouldn't significantly affect them to do so.
You say that the original source code was in the public domain. That's fairly rare; most of the time the original source code is still copyrighted, but available under a free license (and sometimes, code is posted online without any license listed, which actually means that it is copyrighted and no permission is given for you to make any copies of it or modify it in any way). So, be careful that you are not accidentally violating anyone's copyright by modifying and distributing the code, or that you are complying with any license conditions on it if there are any.