No, the Church of Jesus Christ of Latter-day Saints does not practice polygamy anymore, regardless of whether it is legal under local law. See below the declaration made on October 6, 1890 by church President Wilford Woodruff:
Official Declaration 1
The Bible and the Book of Mormon teach that monogamy is God’s standard for marriage unless He declares otherwise (see 2 Samuel 12:7–8 and Jacob 2:27, 30). Following a revelation to Joseph Smith, the practice of plural marriage was instituted among Church members in the early 1840s (see section 132). From the 1860s to the 1880s, the United States government passed laws to make this religious practice illegal. These laws were eventually upheld by the U.S. Supreme Court. After receiving revelation, President Wilford Woodruff issued the following Manifesto, which was accepted by the Church as authoritative and binding on October 6, 1890. This led to the end of the practice of plural marriage in the Church.
To Whom It May Concern:
Press dispatches having been sent for political purposes, from Salt Lake City, which have been widely published, to the effect that the Utah Commission, in their recent report to the Secretary of the Interior, allege that plural marriages are still being solemnized and that forty or more such marriages have been contracted in Utah since last June or during the past year, also that in public discourses the leaders of the Church have taught, encouraged and urged the continuance of the practice of polygamy—
I, therefore, as President of The Church of Jesus Christ of Latter-day Saints, do hereby, in the most solemn manner, declare that these charges are false. We are not teaching polygamy or plural marriage, nor permitting any person to enter into its practice, and I deny that either forty or any other number of plural marriages have during that period been solemnized in our Temples or in any other place in the Territory.
One case has been reported, in which the parties allege that the marriage was performed in the Endowment House, in Salt Lake City, in the Spring of 1889, but I have not been able to learn who performed the ceremony; whatever was done in this matter was without my knowledge. In consequence of this alleged occurrence the Endowment House was, by my instructions, taken down without delay.
Inasmuch as laws have been enacted by Congress forbidding plural marriages, which laws have been pronounced constitutional by the court of last resort, I hereby declare my intention to submit to those laws, and to use my influence with the members of the Church over which I preside to have them do likewise.
There is nothing in my teachings to the Church or in those of my associates, during the time specified, which can be reasonably construed to inculcate or encourage polygamy; and when any Elder of the Church has used language which appeared to convey any such teaching, he has been promptly reproved. And I now publicly declare that my advice to the Latter-day Saints is to refrain from contracting any marriage forbidden by the law of the land.
President of The Church of Jesus Christ of Latter-day Saints.