All in a Night's Work (1961)

It's nice work - and you can get it!

After the sudden death of magazine publisher Colonel Ryder, his nephew, Tony inherits the magazine and has big plans to expand it. While negotiating a loan from the bank, Tony gets a call from a detective surrounding his uncle's death. It turns out Colonel Ryder died in his hotel room with a smile on his face and a young woman was seen fleeing his room wearing only a towel. Suspicious of this woman and afraid the magazine's wholesome image may be tarnished and their loan denied, Tony asks the detective to stick around and find her.