New book alleges Pope John Paul I was victim of a poison plot; In God's Name, by David A. Yallop. New York: Bantam Books. 339 pp. $16.95.

No other of mankind's institutions, not even royalty, has undergone greater tumult or more wrenching vicissitudes than the Roman Catholic papacy. Its Popes have been martyred, assaulted physically, abducted, driven out upon the roads, besieged, and flouted. Yet, notwithstanding that Hitler toyed with the idea of kidnapping Pope Pius XII, such treatment of supreme Pontiffs has, for several centuries, seemed a thing of the past. Has seemed so, that is, until the publication of this book. For if credence can be given to the statements and conclusions in ''In God's Name,'' Albino Luciani, Pope John Paul I, was poisoned in his Vatican bedroom.

This book has two themes. The first is the character of John Paul I, who emerges from these pages as one of the most deeply human Popes of recent centuries. The second is the fear and bitter opposition which the author states arose almost instantly to his liberal and church-purifying motives and which, Yallop tells us, led to his murder. The author traces this opposition to (a) John Paul's determination to remove from office highest-level church officials whom he deemed unworthy; (b) the fact that some of these removals would have both incriminated and ruined dishonest yet enormously influential Italian financiers who had peculated billions of dollars (some of this with help from the so-called Vatican Bank); (c) the fear that John Paul would turn out to be even more liberal than Pope John XXIII, whereas the Vatican establishment yearned for a return to conservatism.

The author tells us that each of these fears was well-grounded. The new Pope had immediately ordered an investigation of Vatican financial transactions. He had ordered that certain high clerics - among them Chicago's John Cardinal Cody, whose imperious actions had scandalized many - be removed from office. He had, if we can again believe the author, given indication that he might even reverse his predecessor's strictures against artificial birth control. And while Patriarch of Venice he had demonstrated his ''abhorrence of a wealthy, materialistic Church,'' having exhorted all clerics under him to sell their precious objects.

The author centers his suspicion in the alleged murder upon five individuals in addition to Cardinal Cody. Of these, one other, Jean Cardinal Villot, Vatican secretary of state, was on a topmost rung of ecclesiastical power but strongly disapproved of John Paul's liberalism. The other four felt threatened because of enormous financial misdealing. They were then Bishop (now Archbishop) Paul Mar-cin-kus, head of the Vatican Bank; Michele Sindona, now serving 35 years in an American prison for financial dishonesty; his partner in crime, Roberto Calvi , who was found hanging beneath a London bridge two years ago; and the most sinister of all, Licio Gelli, called ''the puppetmaster'' for his manipulation of men and events. It is the last whom the author deems likeliest to have arranged the papal assassination.

Lending what many may feel is weight to the charge of murder is the fact that in the decade ending in 1982 investigation into financial wrongdoing of some of the above led to the violent death of six other individuals, the highly suspicious ''suicides'' of three more, and the abortive attempt to murder still another.

The author, who has published four previous investigative books, states that it was unnamed sources in the Vatican itself who asked him to look into the papal death. In fact, other sources, both within the Catholic Church and the Italian press had believed that an investigation was called for. Among the reasons for this were the fact that no definitive death certificate has been produced, no autopsy was performed, and official Vatican sources over the days following the Pope's passing on Sept. 29, 1978, issued an array of self-contradictory statements and, the author alleges, outright falsehoods.

Against all this must be set other instances. Although the Pope's personal physician expressed doubt that the former would die of a heart attack, as officially stated, John Paul had had serious physical problems. All the author's allegations are purely circumstantial without a single item of indisputable proof. The confusion in the Vatican after the Pope's passing is not inconsistent with the turmoil that would arise with the loss of a second Pope within less than eight weeks. Finally, the book has that indefinable yet unmistakable atmosphere of sensationalism which the best of investigative works seek to avoid.

Where does this book leave us?We have certainly been given a startling view into the financial misdoings with which, wittingly or unwittingly, the Vatican Bank was involved. We have seen how Pope John Paul I might well have been considered a peril to some. But, unless at some future date a direct participant in such a crime comes forward, we are lacking credible proof. Perhaps all that can be said is that, like the assassination of President Kennedy, the death of Pope John Paul I will periodically exercise the imagination of historians.

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