There is some dispute about the exact nature of the church in the early years (and, indeed, of its continued existence) because all the records were lost when Providence was burned to the ground in 1676.
In A History of the Baptist Churches in the United States , Albert Henry Newman says that Williams was "a thoroughgoing Calvinist, and most of the original members of the church were probably at one with him in holding to particular redemption and related doctrines." However, he notes that some of the other elders "seem to have early declared themselves in favor of general redemption and related doctrines. Apart from the fact that Calvinism was the system of the persecuting Puritans of England and America, a Socinianized Arminianism represented by the English General Baptists was at this time making rapid headway in England and America, and this type of doctrine soon met with wide acceptance among the Providence and Newport Baptists."
The church eventually split in 1652 over the issue of laying on of hands; Williams had considered laying on of hands essential, and it was popular among the English General Baptists. Apparently it became an issue of fellowship whether laying on of hands was required, with one group insisting that it was; they became Six Principle Baptists, who were Arminian in soteriology.
(Laying on of hands, though associated with the Generals, was not limited to Arminian Baptists. The Philadelphia Baptist Confession of 1742, though Calvinist in soteriology — being identical to the Second London Confession — maintained that "laying on of hands (with prayer) upon baptized believers, as such, is an ordinance of Christ, and ought to be submitted unto by all such persons that are admitted to partake of the Lord's Supper ...")