yes but there are some caveats.
say the total refi was $100 and the old loan of $70 was paid off.
so far only 70/100 of the interest would be schedule A
it took you 4 months after the refi to close on the rental
the interest on 30/100 during this period is not deductible.
if the 30% can be traced to the purchase of the rental then starting with the closing date the interest would go on schedule E. Warning if that $30K was used for something else between the time of the refi and purchase of the rental, deductibility would be in jeopardy.