I assume you meant "short term disability"

If your wife is employed, the short term disability is usually enrolled with a carrier who has a contract with your wife's employer. If your wife has not been enrolled before she is pregnant, ask the HR of her employer to figure out if she is still eligible.

If she's already enrolled, then contact the carrier to inform that she is pregnant and going to take pregnancy leave from xx-xx-xxxx. The carrier will start to pay the benefit from the requested date.

This is a benefit from her employer, not a public charge at all.