Is it OK to ask for my martial status on a credit application?

[Greyat]

What possible relevance can it have.

I'm buying a car. I'm a widow and not keen to tell the dealer that.

I suppose I could put single, but one of the tick boxes is widow, so it wouldn't be correct?

Ask them why they need to know.

You could ask - but may be because someone who is married or living with a partner is potentially lower risk to take on credit as they have a joint income.

Agree with this. Marital status is one way of getting an idea of what kind of risk profile they should assign to you in order to judge your creditworthiness. I'd hope they would qualify this by other factors, like age and home ownership - a single 18 year old is likely to be less creditworthy than an older widow for example.

In GDPR terms it's fine to ask as long as they have a good reason for doing so (eg to judge your creditworthiness), they explain this in their privacy policy, and their privacy policy also explains whether they make any decisions that will affect you using automated means (probably the case here). I believe you may be able to appeal automated decisions somehow, though I've not got any experience of doing so myself.