Can applying 3V damage a sound card?

3V in the mic input does sound like a lot. A microphone only outputs very slight voltage variations, that's why you always need an amp.

Thanks for ur reply. I know 3V is not the usual voltage range of a audio input. But I thought there will be some over voltage protection circuit inside the card. What I want to know it, is it possible to partially damage a sound card( In my case reduced sensitivity)?

Yes absolutely, While the inner components that make up electronic hardware usually either work or don't work It's not unheard of for a stressed inner component (transistors, resistors, capacitors etc.) to have their value changed as a direct result of stress (IE improper voltage, heat, improper grounding, etc.) This changed value can cause issues which might manifest in a myriad of ways including reduced sensitivity.

In your case reduced sensitivity seems to be logical since the area you fed the over-voltage too leads directly to the circuitry responsible for that sensitivity.

I'm sure you suspect this already anyway. I wish I could give you a different answer.