Breakdown:
* nee (நீ) - you
* theey (தீ) - tea
* kudithaaya? (குடித்தாயா?) - did you drink?
Note: This phrase is a bit informal. If you want to be more formal, you can use "saapittaaraa?" (சாப்பிட்டாரா?) which means "did you eat?" and works for both food and drink.