With a smile that has made the front page of many newspapers, photogenic tennis star Hu Na is by now nearly as famous in the United States as in her native China.
The reason: Last summer she defected at a Santa Clara, Calif., match. This week the US granted her ''political asylum'' despite high-level Chinese warnings that Peking may retaliate by reducing cultural exchange programs.
This public rebuff to China follows growing publicity on the Hu Na case. The issue has reopened debate over just what should be the priorities in US policy toward China.
On one side are the promoters of closer ties between the US and China who do not want Peking provoked to the point of lessening athletic, educational, and other cultural relations. On the other side are those who are concerned that the US State Department is tempted to close the door to Chinese asylum seekers, while welcoming as useful propaganda tools applications from Soviet bloc citizens.
The publicity in the Hu Na case increased pressure on the State Department and the White House from conservative backers who have supported President Reagan's policy of arms sales to Taiwan. A rejection of Miss Hu's bid would have left the Reagan administration vulnerable to charges of abandoning its firm policy toward China. On the other hand, tensions with Peking over a host of issues, including arms sales to Taiwan and trade, have left concern that grants of asylum could add one more strain to the relationship.
In recognizing Hu Na's argument that she had ''a well-founded fear of persecution'' in China, the Reagan administration in effect rejected Chinese assurances that Miss Hu would not be punished if she returned to China. The decision also appears to give credence to some of Miss Hu's bleak description of sports life in China.
Miss Hu has claimed that she defected because, as a notable athlete, she was being pressured to join the Communist Party and thus get caught in dangerous factional fighting. In the application she reportedly argued that she was under the pressure of political study sessions aimed at improving her tennis in harmony with Marxist-Leninist principles. To some China specialists, this revived memories of the 1960s and '70s, when prominent Chinese athletes were promoted by one political faction, only to be purged and sometimes sent to forced labor when the sponsoring faction fell from power.
The Hu Na case stands out because it contrasts with the quiet, diplomatic method generally followed by China and the US in cases where Chinese in the US choose to stay on.
There are now some 10,000 Chinese students and scholars in the US (split about evenly between privately sponsored and government-sponsored students), according to the State Department. Since 1979, hundreds of such Chinese students and scholars have stayed on in the US after their periods of study or work were over. For many of these relatively young and privately sponsored students, the private F-1 visa can be smoothly adjusted without applying for ''political asylum.''
Since 1979, some 10 mainland Chinese have been granted ''political asylum'' in the US out of 300 or 400 applications, according to one well-placed source. Of more than 1,000 pending applications from Chinese asylum seekers, the number of applicants from mainland China has not been separately classified according to the State Department. The State Department says, however, that a ''large proportion'' are from Taiwan and Hong Kong.
Asylum applications are made privately, and there is no public discussion. This is to ensure that if asylum is denied, the applicant is less likely to be punished after returning to China. Also, if the US denies asylum, the applicant can arrange to go to a third country, instead of returning to China. Decision on asylum bids can be put off indefinitely, and until there is a final decision, the applicant may remain in the US.
A Chinese Embassy official in Washington says China had long expected that a number of privately sponsored students would stay on in the US for a variety of reasons. But China takes a different position on the often older, officially sponsored Chinese with the J-1 visa. ''These people owe it to their country to come home. We spend $5,000 to $10,000 a year on them, so it is not fair for them just to run off,'' he says.
Moreover officially sponsored Chinese are considered less likely to stay because they are usually older, with more professional and family ties at home. Also, unlike the F-1 visa, the J-1 cannot be adjusted for a longer stay without the approval of the Chinese government. Thus, for those on the J-1, the only way to stay may be to apply for ''political asylum.''
This requires the Immigration and Naturalization Service to rule, with State Department advice, that the applicant has ''a well-founded fear of persecution based on race, religion, nationality, group membership, or political opinion.''