Per the CBOE margin manual - here's the minimum margin requirements (your broker may require higher):
Initial and maintenance margin are the same - 100% of option proceeds/market value plus 15% of underlying broad based index value (or 20% of underlying stock or narrow based index) less out of the money amount if any to a minimum of option premium plus 10% of put's exercise price
Note that most brokers will have different trader/account qualifications for shorting puts and calls (which will usually be much more strict).
Various other margin rules if you put on positions in combinations - e.g., a short staddle (short a put and a call) has margin requirement that is either the requirement of the short put or short call whichever is greater plus the option proceeds/market value of the other side (so it's less than the sum of the seperate short put and short call margin requirements).