In any case, this is what various sources say. In my unpublished manuscript on the life and teachings of Joseph Smith, I have worked hard with the three witnesses of the Book of Mormon and found out a few things. Here is an example:
As early as 1835, the beginning of the rift between the two friends and relatives, Joseph Smith Jun. and Oliver Cowdery began to develop. This was due to the relationship of Joseph Smith, who was already married to Emma, which he had with one of his maids, Fanny Alger (then 16 years old), and which he had taken as a second wife in the same year, also before his wife Emma, and Oliver rightly accused him of adultery. On January 21, 1838, he wrote about it to his brother, reiterating his accusations against Joseph Smith Jun., calling the relationship a "dirty, disgusting, dirty affair." For the first time, Oliver Cowdery opposed the "prophet", citing not only the affair with Fanny Alger, but also the fact that Joseph Smith, in his opinion, would care too much about worldly affairs (e..B g. the Kirtland Bank) as the spiritual affairs. This rift, and because Oliver Cowdery had his heart on his tongue, ultimately led to him being expelled on April 12, 1838. The reason for this exclusion was not on the basis of what Oliver Cowdery brought against Joseph Smith Jun., but on the fact that he had been inactive in the Church and was a lawyer against the Church for his clients, because they wanted damages from the Church for their losses in the bankruptcy of Kirtland Bank. (...)
Oliver Cowdery left the church because he rightly felt he had been treated unfairly, and he was also very hurt and upset at the way his allegations against Joseph Smith Jun. had been handled. He finished his law degree, and worked as a lawyer, first in Kirtland, Ohio, then, from 1840 in Tiffin, Ohio, from where he eventually moved to Wisconsin in 1847. Politically, he served in the Democratic Party for which he wanted to run for Congress. But when it became known that he was one of the three witnesses to the Book of Mormon fraud, he was caricatured in the newspapers and lost the election on which he had placed such high hopes.
A reference in a poem written in Times & Seasons, Volume 2, 482, states that Oliver Cowdery later denied his testimony of the Book of Mormon. He became a member of a Methodist church in Tiffin after his excommunication, and had long since said goodbye to Mormonism. In this Church he served in various callings (Superintendent of the Sunday School and Secretary), and was a recognized member of his Church (D. Michael Quinn: The Mormon Hierarchy: Origins of Power, Signature Books, 1994, p.545).
Even during his excommunication, Oliver Cowdery remained in friendly contact with some Mormons. In these letters he lamented above all the intolerance of the church leadership of dissidents, as well as the practice of polygamy (more on this subject later). His desire to be a member of the Mormons again, where he was someone, grew stronger in 1848, and so he traveled to Winter Quarters, Nebraska, to visit and talk to Brigham Voung, the new Mormon prophet after the death of Joseph Smith. On November 12, 1848, after spending hours of interrogation, he was baptized again by Orson Hyde, a Mormon apostle, but did not regain his previous functions. Why did he be braised? Where he never fully reconciled with the Mormons, and many of the Mormons opposed his baptism? The Gospel Herald of November 1, 1849 writes about it:
"You can still see that they never mention Oliver Cowdery as one of them. In truth, he is not a man for them. It was a strange bout of mania that led him to them, and seems to have lasted only a few weeks for him ... in no single moment did they confer any power on him." (Cited in Jerald & Sandra Tanner: Case Against Mormonism, 1968, p.28.)