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Not only is it impolite, it might actually be cause for being fired on the spot. Even if you are leaving and on your notice period, you are still a contracted employee and you are still required to do the tasks asked of you.

Nothing changes in that regard until you actually leave. Whether or not you work on your existing tasks, handover, or new things assigned to you, is really up to the company. If they decide you need to do zero handover and instead start on a new project despite you not being able to finish it, that's... well, kinda dumb on their part, but it's not your problem.

You can advise them that you need time for handover, but they set your tasks while you work for them. Once your contract runs out, you just leave and the current state of their affairs is their problem to do deal with.

Is it impolite/rude to reject new tasks and just finish my ongoing tasks?

It is unprofessional.

How should I say I don't want to do new tasks as I'm leaving
the company and of course working on new tasks take longer than normal

You don't say that. That is for the company to decide.
There are two things.

• They assign a job to you. You need to calculate the estimated time and the percentage of work you can do till you are with the company; if there is any backlog from the previous project or knowledge transfer to be done, you need to consider time taken for that as well and give them a clear picture of how much % of work you'll be able to complete. When all the statistics are given, it is upto them to decide whether to assign you a new task or not. Mostly, they won't. Even if they do, take it up, but be upfront about how much you can complete it.




• They don't assign you a job. Be a little proactive and tell them in advance the amount of time you have with you and ask them for a job that can be done during this time.

In both the cases, you are deferring the decision to them and you are only suggesting. This is important.

Erik and WonderWoman already answered clearly, but omitted one thing:

Yes, you are still under contract and all the obligations of your working contract are still in place, including that they give you tasks to do.

However, it is professional to consider the fact that you are leaving. If you estimate that a task will not be completed by the time you leave, or requires investments into you that the employer will not recover (e.g. learning a new skill), it would be right to point this out to them. Not as a reason to refuse, but as something to consider.

Another thing to consider is tasks that involve clients. If a task requires you to establish contact with a client who doesn't already know you, it can reflect poorly on the company if the next time someone else calls. It might be better for the company to have whoever will be doing the job after you contact them instead.

All of these things are theirs to decide, but some of them are easier to see for you, and thus you should point them out. The idea is to be cooperative and helpful and leave in a positive way. You never know when a positive recommendation from this company might help your career in the future.

You should agree on when you will stop working for them and when they will stop paying you. You should do whatever work is asked of you, within reason, until that time. For whatever time you have agreed, or do agree, to work, you should work as hard as you normally would. If you are asked to do things you won't be able to finish, you should inform your manager.

Things that are unprofessional for you:

1. Not making every effort to agree on a reasonable end date.


2. Agreeing to work until a certain date and not actually working until that date.


3. Expecting to get paid for time you are not working unless agreed.


4. Not letting your employer know what work they can reasonably expect from you given the amount of time you have left.

Things that are unprofessional for your employer:

1. Not making every effort to agree with you on a reasonable end date.


2. Expecting you to do more work than you would normally do.

How should I say I don't want to do new tasks as I'm leaving the company

Answer:

You don't (directly) say that.

But it is the wrong question to ask - and you won't need to say it if you do this:

Leave in a "professional manner"

1. Before you resign, prepare a list of things that you need to wrap up and estimate how long each of these tasks will take (in hours). Include a list of things you cannot complete.




2. Provide this list to your manager (pad your estimates) when you resign. Your resignation should also be in writing and hand delivered in person if that is practical (won't work for long distance telecommuting).




3. Ask your manager to re-prioritize it for you if s/he desires.




4. As you work through your TODO list, make sure you have enough time to finish what is left on it. If you don't have enough time, immediately mention this to your manager and ask which items should be dropped (stop the current thing? Ignore the last three items on the list?).

Number 4 also works for items that your manager adds to your list.

Don't agree to any new work from anyone except your manager.

Sample response to someone who isn't your manager: "I can see how that would be useful. I will check with [manager name] to verify which items can be dropped from my current plan so I will have time to do that."

5. Keep up with the number of hours you spend on each task on the list. Keep manager informed as often as needed (generally as you finish each task, but no more often than the end of each day).




6. Finally, if your manager assigns you new things, as bad an idea as this is, you do it anyway because they are your manager.

While employed, it is of course at all times your job to do best you can by the company, but in situations like this, focusing on knowledge transfer, documentation, eradication of tech debt and smooth transition of responsibility for previous work may be doing just that.

Still, I'd just present this point of view to the company and let them decide how you should best use your remaining time.

Yes, it's impolite, and it's also career-limiting.

You want to be well-remembered upon leaving your company. You want the last impression that people have of you to be a positive one, because that will be the most lasting. If you start refusing work in your last days at your job, that's how you're going to be remembered.

You never know when your past employees might wind up being a reference for you, officially or otherwise. You don't want one of your co-workers to be asked about you and they reply "Oh, that guy? He was OK, but then he refused to do any work once he put in notice."