Simon Brett 
The Liar in the Library 

Fethering has everything a sleepy coastal town should: snug English pubs, cosy cottages, a little local library – and the occasional murder . . .Bestselling author Burton St Clair, complete with soaring ego and wandering hands, has come to town to give a talk. But after his corpse is found slumped in his car, he won’t be leaving. Jude is the prime suspect; she was, after all, the last person to see Burton St Clair alive. If she is to prove her innocence, she will have to dust off her detective skills and recruit her prim and proper neighbour (and partner-in-sleuthing) Carole to find the real culprit.