The body of a 34-year-old woman was discovered at around 4pm on Sunday near Llanidloes.
A 46-year-old man was arrested on suspicion of murder later that day. He remains in police custody.
Dyfed-Powys Police has said officers are keen to speak to anyone who may have witnessed, or has dashcam footage of, a man and a woman in the town, or on the A470 between Llanidloes and Dolwen, on Saturday or Sunday.
The woman is described as white, 5ft 4ins, of small build, with very long dreadlocks, which were past her waist. She was wearing a grey coloured top, dark trousers and white trainers.
Police would also like to speak to the person who gave the man and his dog a lift between Welshpool and Shrewsbury, dropping him off near the Dinky’s Dinahs layby in Ford on Sunday.
Officers are not currently looking for anyone else in connection with this matter.
Anyone who may have information that could assist the investigation is asked to get in touch online through the dedicated Public Portal.
You can also contact police by calling 101. If you are deaf, hard of hearing, or speech impaired text the non-emergency number on 07811 311 908.
Alternatively, contact the independent charity Crimestoppers anonymously by calling 0800 555111, or visiting crimestoppers-uk.org. Quote reference: DP-20230528-120.