Question: Some studies have shown that serif versus sans-serif on a computer display is not what affects readability and the practical differences between the two font styles are largely inconclusive.

I observed some designers prefer to use serif fonts only for titles or important elements and that make me ask: The font style on a CTA affect user's decisions?

Answer: 
According to [this](https://blog.kissmetrics.com/how-typography-affects-conversions/) post by Kissmetrics:

> 
> As far as research goes, there is no ironclad answer as to whether serif or sans serif is better. But, as far as general consensus goes, when it comes to reading online, sans serif typefaces are easier to read because they are simple and legible even in small sizes. This means people can spend more time focusing on the message than deciphering the typeface.
>  Sans serifs are recommended for the body of the copy and serifs for the title and subtitles.
> 
> 
> 

We can arrive a conclusion that sans serif typefaces are better for CTA moments, where people need to spend more on focusing on the message (and in this case, the message that your CTA trigger needs to give).
"Will serif or sans-serif fonts change the user decision/behavior on a call-to-action?"

The short answer is no. The serif may affect readability, and there is something to be said about aesthetics, but at the time of this post (2017) there is no conclusive evidence that a serif font influences user decisions. 

The rule of thumb is that sans-serif is more readable for small text and digital reading (think eBook). Serif fonts can help readability in "real world" tangible books (rumor has it these still exist in buildings called libraries). Most Call-to-Actions are some form of the button or smaller element on the page and thus do not contain large text, therefore sans-serif is probably the way to go.

However, largely differing font families (whether serif or not) can create different impressions on the user. Imagine if Amazon changed its font sitewide to Lucinda Cursive or something radical -- at the aggregate level, analytics would quickly show that user behavior is affected. 

Hope this helps to clarify.