There are many different types of Christian church, and within each local church there will be a varied and diverse membership. Consequently, there are likely to be many ways in which you could invite a local church to become involved with your school, to the benefit of the pupils.
It is quite probable that amongst your staff and pupils, there will be a number of Christians who belong to local churches. You could start by asking them for contacts if you want to get in touch with a local church leader to see whether your school could benefit from contributions and support from church members. Otherwise, check which Anglican (Church of England) parish your school is located in and start by contacting the local vicar.
Alternatively, there may be a church belonging to another main denomination nearby, e.g. Baptist, Methodist, Catholic, where you could enquire. Or ask other headteachers which churches or Christian groups support their school. Sometimes the smaller, more informal churches have a lot to contribute to schools, but their very informality (not belonging to a main denomination) makes them harder to contact. Internet searches can be useful in this respect. If it is a church you have never heard of, check it out with Christians on your staff or other local headteachers.
A short meeting with the church leader will help you decide whether the church has something to offer to you. Typically, a church may be able to support teaching and learning in RE or PSHE, or make contributions to meaningful collective worship. Church members may have expertise to offer in science, art, music, foreign languages and technology amongst other subjects. But they may also be able to support by becoming governors, mentors for pupils, volunteers for lessons and school trips and with out-of-hours and extra-curricular activities.
Many church members will already be CRB checked, but you must ensure that your own school policy is implemented in this area. Any church members coming into schools may need an induction into the school, but will certainly need to be welcomed and made familiar with the facilities available and shown the location of toilets and drinks. There should always be a staff member responsible for the visitor, otherwise health and safety and insurance issues may arise. Visitors should never have to contend with behaviour management issues; that responsibility lies with the staff member.