HONG KONG is drawing thousands of East European visitors annually and most of the 13,000 visitors last year came as tourists or in search of business. However, only a ''handful'' of those liberated after the demise of communism have chosen to live in the territory. Immigration Department figures show a 52 per cent rise last year in visitors from Eastern Europe. Last year's visitor intake increased by 4,445 from the 1992 influx - and by 12,000 from the number of tourists who came in 1984 when the territory's tight entry rules were first partially relaxed. The figures comprise tourists from Albania, Bulgaria, Czech Republic, Slovakia, Commonwealth of Independent States, Estonia, Latvia, Lithuania, Hungary, Poland, Romania and Turkey. However, the biggest numbers come from Russia. A government spokesman said yesterday officials were coping with the rapid surge in visitors. He stressed procedures for screening criminals were operating effectively. ''We always work closely with police in preventing known criminals from arriving here from overseas,'' he said. ''If they are arrested in Hong Kong, we have a set of procedures in place to effect their removal. ''We are quite vigilant in monitoring visitors from East Europe. ''So far, they have been no problem for us.'' Before September 1992, the Government enforced a restrictive policy virtually barring the entry of visitors from former Soviet bloc nations. However, a review concluded that unreferred visas should be issued. A 14-day visa can be obtained by approaching British Consulate offices in the applicant's country. Appeals for extensions are also able to be lodged in this manner.