Jennifer Lopez sang ‘‘Happy Birthday’’ to the leader of Turkmenistan during a show, but her representative said she wouldn’t have performed there at all if she had known there were human rights issues in the country. The singer and actress performed in the former Soviet bloc country on Saturday night. A statement released Sunday by her publicist to The Associated Press said the event was hosted by the China National Petroleum Corp. and wasn’t a political event. However, the country’s leader, Gurbanguly Berdimuhamedow, did attend. Berdimuhamedow has been criticized for oppressive rule by human rights organizations. Human Rights Watch describes Turkmenistan as ‘‘among the most repressive in the world.’’ After a United Nations visit last month, Assistant Secretary-General for Human Rights Ivan Simonovic said the country had made progress in the area of human rights, but ‘‘a lot more work is needed to . . . ensure practice is in line with international standards.’’ Lopez’s publicist says the event was vetted by Lopez’s staff: ‘‘Had there been knowledge of human rights issues any kind, Jennifer would not have attended.’’ The birthday serenade was a last-minute request made by the corporation to Lopez before she took the stage, and she ‘‘graciously obliged,’’ the statement said.