The jury in the second murder trial of Wilfredo Santiago in the execution-style slaying of Police Officer Thomas Trench in 1985 completed its first full day of deliberations yesterday without reaching a verdict.

Many of the witnesses in the case suffered credibility problems, and the jury has the unenviable task of deciding what was true.

No physical evidence or eyewitnesses linked Santiago, now 44, to Trench's killing, and the prosecution's case has depended on circumstantial evidence.

Prosecutors have argued that Trench, 43, was shot in the face and neck in a case of mistaken identity as he sat in his patrol car at 17th and Spring Garden Streets on May 28, 1985. Officials contend that Santiago had a grudge against another officer who had been driving the same patrol car in the previous shift and was gunning for him when he shot Trench.

A jury convicted Santiago in 1986, but an appeals court ordered a new trial in 1991 because of judicial misconduct. The first scheduled retrial was called off when a judge ruled that the prosecution's conduct in the first trial was so egregious that it would be wrong to subject Santiago to another proceeding. An appeals court overturned that decision in 1994, but a series of appeals and motions delayed the retrial until this year.