In my area you are offered a triple test at 16 weeks regardless of age, its a blood test that tests your risk of things like downs and spina bifida, if these results are high you are offered an amnio, from talking to people when i was pregnant this happens in a lot of areas.
Amnios are generally not offered to people under 35 as the risk is very low
I was offered one and Im only 25, 1st baby and not high risk. They do it by blood now a days not the big needle in the belly. If blood shows any risk they investigate further with the big needle.
The amnio IS the needle test. All women are offered or can ask for the blood test which will asses the risk. If it's high for your age then they will offer the amnio.