TURNOVER in index futures burst through 30,000 contracts yesterday as roll-over activity from April to May grew a pace. Overall market volume was 31,654 contracts. The April future, which expires tomorrow, rose 175 points to 9,340, as did the May contract. Turnover in April was 17,825 lots and in May it was 13,829. The close of futures left them at an 11-point premium to the cash. Estimated open interest in April is 20,185 contracts and in May it was 14,212. Jardine Fleming said: ''In spite of the bullish activity in futures, bears dominated the options market and sold more call premium in the May 9,600 calls while the June 8,400 puts were actively bought.'' This depressed implied volatility to 35 per cent in May for at-the-money calls and puts. In June they were 34 per cent and 35 per cent respectively and September they were 33 per cent and 35 per cent respectively. All this happened on pretty thin volume of 1,328 lots, just 4.2 per cent of futures volume. Open interest was 32,270 lots. The lacklustre activity in options is causing some dealers to be concerned about the viable level of liquidity to maintain a buoyant market.