I gather you have two counts, and which could have been anything (i.e., they are not bounded—counts of successes out of a total number of trials). The simplest distribution of counts is the Poisson, but there can be other, more complicated, distributions as well (e.g., negative binomial). With your data, you cannot differentiate between different possible count distributions. You can assume they are Poisson, but that's it, and if that assumption is incorrect, your results will be invalid.
In addition, when people model counts, there is often a variable that indicates some kind of opportunity for an event to occur. That's what you have as "Patient Days", I gather. We adjust for this using an offset.
Thus, it is possible to have a (rather low powered) test of your data by assuming they are realized values from a single Poisson distribution and adjusting with an offset, and seeing if that looks reasonable. In R, this can be done with the ?poisson.test function:
poisson.test(x=c(61, 41), T=c(102000, 110000))
# Comparison of Poisson rates
# data: c(61, 41) time base: c(102000, 110000)
# count1 = 61, expected count1 = 49.075, p-value = 0.02222
# alternative hypothesis: true rate ratio is not equal to 1
# 95 percent confidence interval:
# 1.062580 2.445082
# sample estimates:
# rate ratio