I see that the relationship will be positive, i.e., companies that in corporate CSR in their policy and strategy would have a higher CSP. The rationale is simply in the CSR is one of the elements of CSP.
I am attaching herewith some literature that discusses CSP and CSR:
My research shown that the effect of CSR on the CSP was negative. This is probably due investors are not interested in the social news because there is another data that can be obtained as a consideration in the decision making.
CSP is an extension of the concept of CSR. That focus on Actual Results achieved rather than general idea or belief of businesses or responsibility to society.
Corporate Social Performance (CSP) is an extension of corporate social responsibility (CSR), with focus on actual results or outcomes achieved by organizations who are believed to be responsible and accountable. it is the identifiable and measurable structural categories of business activities' impact on the stakeholders, the society and the organization itself.