Would it be legal to repeat an exam that has been cleared from another state

You can repeat your 10th class again in Assam.
You can opt for the CBSE syllabus if you passed earlier in the State syllabus.
If you studied already in CBSE, you can opt for the State syllabus now.
You can use the second certificate which is the latest certificate. There is no problem with having two certificates for the 10th class.
You can appear as a private student and write the examination.

Yes definitely you can re-appear for the class 10th exam and it will be considered completely legal. In many states it is a rule that in order to get some facilities, it is necessary that your education has been completed in the same state and this is not the case, then the state law gives you a chance you can repeat the board examinations like this. Huh. Many times there have also been cases for jobs, where if a person from another state wants a job in a remote state, then he has to pass the 10th or 12th examination of that state, only then he will be considered eligible for the job. So be sure to re-appear in your 10th exam, it will not cause any kind of problem. For more information, you can also take personal information from the concerned state board.

While considering your case for the reappearance of class ten again, there would not be any problem if you want to pass this examination by sitting either through the State Board of Assam if not taken up earlier. This facility will be applicable to you even if you have passed your class ten Board Examination through the CBSE Board. Vice versa is applicable in your case.
What is needed from your end is to go through the syllabus of the Board with which you want to pursue your examination. For the better understanding of the basics, you may take up the help of experienced teachers to understand the fundamentals of the subjects. If required, you may join a reputed institution operating near your locality to perform better in the class ten Board Examination.

This is a tricky situation and requires some more understanding of the issue. Generally the purpose of re-examination is for the improvement. If you had less marks in an exam the you are given an opportunity to reappear in it for improvement and then out of the two the better one is to be presented by you wherever they are required for admission or selection process. So the marks obtained in the second exam for the same class are to be considered for the admission if they are more than the earlier marks.
In this case you are doing it for your inclusion in the basic eligibility criterion that you should have done class 10 from Assam and now you are doing it at a later time. So the Assam state education department must clarify this whether they would agree to the second exam undertaken today for that purpose. So I advise you to get it cleared from them. There are some administrative points which are required to be understood and if they allow it then there is no problem.