No, it is not mandatory that you should undergo Down Syndrome screening. You can understand about Down Syndrome and the detection tests available, and then you can decide if you want to undergo the screening test.
Remember screening tests are indirect. A screen positive result does not mean the baby is affected. A screen positive test only indicates that a further confirmatory test may be required.
Another important thing to remember is that no screening test can detect all cases of Down syndrome. This means that when the indirect test says screen negative, it says that the chance of the baby having Down syndrome is very low.
In short, a properly conducted FTS or a QST along with a normal target scan can reliably reassure most women. However, the choice of undergoing the screening test is always yours.